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Volumn , Issue , 2008, Pages 417-491

Harmonic maps: Dedicated to the memory of James Eells

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EID: 78650027519     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452833-9.50009-7     Document Type: Chapter
Times cited : (86)

References (240)
  • 1
    • 0000712349 scopus 로고
    • On n-dimensional problems in the calculus of variations in the large
    • Al'ber S.I. On n-dimensional problems in the calculus of variations in the large. Sov. Math. Dokl 1964, 5:700-704.
    • (1964) Sov. Math. Dokl , vol.5 , pp. 700-704
    • Al'ber, S.I.1
  • 2
    • 0011260111 scopus 로고
    • Spaces of mappings into a manifold with negative curvature
    • Al'ber S.I. Spaces of mappings into a manifold with negative curvature. Sov. Math. Dokl 1967, 9:6-9.
    • (1967) Sov. Math. Dokl , vol.9 , pp. 6-9
    • Al'ber, S.I.1
  • 3
    • 0000429803 scopus 로고
    • Co-area, liquid crystals, and minimal surfaces
    • Springer, Berlin, Tianjin, 1986, Lecture Notes in Math., 1306
    • Almgren F., Browder W., Lieb E.H. Co-area, liquid crystals, and minimal surfaces. In: Partial differential equations 1988, 1-22. Springer, Berlin, Tianjin, 1986, Lecture Notes in Math., 1306.
    • (1988) In: Partial differential equations , pp. 1-22
    • Almgren, F.1    Browder, W.2    Lieb, E.H.3
  • 4
    • 0000678970 scopus 로고
    • Singularities of minimizing harmonic mappings from the ball to the sphere: examples, counterexamples and bounds
    • Almgren F., Lieb E.H. Singularities of minimizing harmonic mappings from the ball to the sphere: examples, counterexamples and bounds. Ann. of Math., (2) 1988, 128(3):483-530.
    • (1988) Ann. of Math., (2) , vol.128 , Issue.3 , pp. 483-530
    • Almgren, F.1    Lieb, E.H.2
  • 5
    • 0001596880 scopus 로고
    • Equations différentielles nonlinéaires et problème de Yamabe concernant la courbure scalaire
    • Aubin T. Equations différentielles nonlinéaires et problème de Yamabe concernant la courbure scalaire. J. Maths. Pures et Appl 1976, 55:269-296.
    • (1976) J. Maths. Pures et Appl , vol.55 , pp. 269-296
    • Aubin, T.1
  • 6
    • 0002308456 scopus 로고
    • A conservation law for harmonic maps
    • Springer, Berlin, Symposium Utrecht, 1980, Lecture Notes in Mathematics
    • Baird P., Eells J. A conservation law for harmonic maps. In: Geometry 1981, 894:1-25. Springer, Berlin, Symposium Utrecht, 1980, Lecture Notes in Mathematics.
    • (1981) In: Geometry , vol.894 , pp. 1-25
    • Baird, P.1    Eells, J.2
  • 8
    • 18344374835 scopus 로고
    • The solution of partial differential equations by means of definite integrals
    • Bateman H. The solution of partial differential equations by means of definite integrals. Proc. London Math. Soc 1904, 1(2):451-458.
    • (1904) Proc. London Math. Soc , vol.1 , Issue.2 , pp. 451-458
    • Bateman, H.1
  • 9
    • 0042802109 scopus 로고
    • The Dirichlet problem for harmonic maps from the disk into the Euclidean n-sphere
    • Benci V., Coron J.-M. The Dirichlet problem for harmonic maps from the disk into the Euclidean n-sphere. Ann. Inst. H. Poincaré, Anal. Non Linéaire 1985, 2(2):119-141.
    • (1985) Ann. Inst. H. Poincaré, Anal. Non Linéaire , vol.2 , Issue.2 , pp. 119-141
    • Benci, V.1    Coron, J.-M.2
  • 12
    • 0041740018 scopus 로고
    • The approximation problem for Sobolev maps between manifolds
    • Bethuel F. The approximation problem for Sobolev maps between manifolds. Acta Math 1991, 167:167-201.
    • (1991) Acta Math , vol.167 , pp. 167-201
    • Bethuel, F.1
  • 13
    • 0000738731 scopus 로고
    • On the singular set of stationary harmonic maps
    • Bethuel F. On the singular set of stationary harmonic maps. Manuscripta Math 1993, 78(4):417-443.
    • (1993) Manuscripta Math , vol.78 , Issue.4 , pp. 417-443
    • Bethuel, F.1
  • 14
    • 0000473878 scopus 로고
    • Regularity of minimizers of relaxed problems of harmonic maps
    • Bethuel F., Brezis H. Regularity of minimizers of relaxed problems of harmonic maps. J. Funct. Anal 1991, 101:145-161.
    • (1991) J. Funct. Anal , vol.101 , pp. 145-161
    • Bethuel, F.1    Brezis, H.2
  • 15
    • 0001943665 scopus 로고
    • Relaxed energies for harmonic maps
    • Birhäuser, H. Berestycki, J.-M. Coron, I. Ekeland (Eds.)
    • Bethuel F., Brezis H., Coron J.-M. Relaxed energies for harmonic maps. Variational Methods 1990, Birhäuser. eds. H. Berestycki, J.-M. Coron, I. Ekeland (Eds.).
    • (1990) Variational Methods
    • Bethuel, F.1    Brezis, H.2    Coron, J.-M.3
  • 17
    • 0002547774 scopus 로고
    • Density of smooth functions between two manifolds
    • Bethuel F., Zheng X. Density of smooth functions between two manifolds. J. Funct. Anal 1988, 80(1):60-75.
    • (1988) J. Funct. Anal , vol.80 , Issue.1 , pp. 60-75
    • Bethuel, F.1    Zheng, X.2
  • 18
    • 0000024406 scopus 로고
    • Dynamical systems with two degrees of freedom
    • Birkhoff G.D. Dynamical systems with two degrees of freedom. Trans. Amer. Math. Soc 1917, 18:199-300.
    • (1917) Trans. Amer. Math. Soc , vol.18 , pp. 199-300
    • Birkhoff, G.D.1
  • 21
    • 0037396143 scopus 로고    scopus 로고
    • Analysis and topology in some nonlinear PDE problems
    • Brezis H. Analysis and topology in some nonlinear PDE problems. Bull. Amer. Math. Soc 2003, 40(2):179-201.
    • (2003) Bull. Amer. Math. Soc , vol.40 , Issue.2 , pp. 179-201
    • Brezis, H.1
  • 22
    • 0000245313 scopus 로고
    • Large solutions for harmonic maps in two dimensions
    • Brezis H., Coron J.-M. Large solutions for harmonic maps in two dimensions. Comm. Math. Phys 1983, 92:203-215.
    • (1983) Comm. Math. Phys , vol.92 , pp. 203-215
    • Brezis, H.1    Coron, J.-M.2
  • 23
    • 84990602658 scopus 로고
    • Multiple solutions of H-system and Rellich's conjecture
    • Brezis H., Coron J.-M. Multiple solutions of H-system and Rellich's conjecture. Comm. Pure Appl. Math 1984, 37:149-187.
    • (1984) Comm. Pure Appl. Math , vol.37 , pp. 149-187
    • Brezis, H.1    Coron, J.-M.2
  • 25
    • 0013234663 scopus 로고    scopus 로고
    • Topology and Sobolev spaces
    • Brezis H., Li Y. Topology and Sobolev spaces. J. Funct. Anal 2001, 183:321-369.
    • (2001) J. Funct. Anal , vol.183 , pp. 321-369
    • Brezis, H.1    Li, Y.2
  • 28
    • 84972503061 scopus 로고
    • Conformal and minimal immersions of compact surfaces into the 4-sphere
    • Bryant R.L. Conformal and minimal immersions of compact surfaces into the 4-sphere. J. Diff. Geom 1982, 17:455-473.
    • (1982) J. Diff. Geom , vol.17 , pp. 455-473
    • Bryant, R.L.1
  • 29
    • 0010564036 scopus 로고    scopus 로고
    • Harmonic morphisms with fibers of dimension one
    • Bryant R.L. Harmonic morphisms with fibers of dimension one. Comm. Anal. Geom 2000, 8:219-265.
    • (2000) Comm. Anal. Geom , vol.8 , pp. 219-265
    • Bryant, R.L.1
  • 30
    • 0007290107 scopus 로고
    • Harmonic maps of finite energy from non-compact manifolds
    • Burstall F.E. Harmonic maps of finite energy from non-compact manifolds. J. London Math. Soc 1984, 30:361-370.
    • (1984) J. London Math. Soc , vol.30 , pp. 361-370
    • Burstall, F.E.1
  • 31
    • 0041093822 scopus 로고
    • Nonlinear functional analysis and harmonic maps
    • University of Warwick
    • Burstall F.E. Nonlinear functional analysis and harmonic maps. thesis 1984, University of Warwick.
    • (1984) thesis
    • Burstall, F.E.1
  • 32
    • 84941838228 scopus 로고
    • Harmonic tori in spheres and complex projective spaces
    • Burstall F.E. Harmonic tori in spheres and complex projective spaces. J. Reine Angew. Math 1995, 469:146-177.
    • (1995) J. Reine Angew. Math , vol.469 , pp. 146-177
    • Burstall, F.E.1
  • 33
    • 0001430673 scopus 로고
    • Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras
    • Burstall F.E., Ferus D., Pedit F., Pinkall U. Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras. Annals of Math 1993, 138:173-212.
    • (1993) Annals of Math , vol.138 , pp. 173-212
    • Burstall, F.E.1    Ferus, D.2    Pedit, F.3    Pinkall, U.4
  • 34
    • 0031509043 scopus 로고    scopus 로고
    • Harmonic two-spheres in compact symmetric spaces
    • Burstall F.E., Guest M.A. Harmonic two-spheres in compact symmetric spaces. revisited Math. Ann 1997, 309(4):541-572.
    • (1997) revisited Math. Ann , vol.309 , Issue.4 , pp. 541-572
    • Burstall, F.E.1    Guest, M.A.2
  • 36
    • 84972528644 scopus 로고
    • Minimal immersions of surfaces in Euclidean spheres
    • Calabi E. Minimal immersions of surfaces in Euclidean spheres. J. Diff. Geom 1967, 1:111-125.
    • (1967) J. Diff. Geom , vol.1 , pp. 111-125
    • Calabi, E.1
  • 37
    • 84936486933 scopus 로고
    • Heat flow and boundary value problem for harmonic maps
    • Chang K.C. Heat flow and boundary value problem for harmonic maps. Ann. Inst. Henri Poincaré Analyse Non Linéaire 1989, 6(5):363-395.
    • (1989) Ann. Inst. Henri Poincaré Analyse Non Linéaire , vol.6 , Issue.5 , pp. 363-395
    • Chang, K.C.1
  • 38
    • 84972521494 scopus 로고
    • Finite time blow up of the heat flow of harmonic maps from surfaces
    • Chang K.C., Ding W., Ye R. Finite time blow up of the heat flow of harmonic maps from surfaces. J. Diff. Geom 1992, 36:507-515.
    • (1992) J. Diff. Geom , vol.36 , pp. 507-515
    • Chang, K.C.1    Ding, W.2    Ye, R.3
  • 40
    • 0039346163 scopus 로고
    • Sobolev inequalities involving divergence free maps
    • Chanillo S. Sobolev inequalities involving divergence free maps. Comm. Partial Differential Equations 1991, 16:1969-1994.
    • (1991) Comm. Partial Differential Equations , vol.16 , pp. 1969-1994
    • Chanillo, S.1
  • 41
    • 0002369805 scopus 로고
    • The weak solutions to the evolution problems of harmonic maps
    • Chen Y. The weak solutions to the evolution problems of harmonic maps. Math. Z 1989, 201:69-74.
    • (1989) Math. Z , vol.201 , pp. 69-74
    • Chen, Y.1
  • 42
    • 51249169799 scopus 로고
    • Remarks on approximate harmonic maps
    • Chen Y., Lin F.H. Remarks on approximate harmonic maps. Comment. Math. Helv 1995, 70(1):161-169.
    • (1995) Comment. Math. Helv , vol.70 , Issue.1 , pp. 161-169
    • Chen, Y.1    Lin, F.H.2
  • 43
    • 0002521307 scopus 로고
    • Existence and partial regularity results for the heat flow for harmonic maps
    • Chen Y., Struwe M. Existence and partial regularity results for the heat flow for harmonic maps. Math. Z 1989, 201(1):83-103.
    • (1989) Math. Z , vol.201 , Issue.1 , pp. 83-103
    • Chen, Y.1    Struwe, M.2
  • 46
  • 49
  • 50
    • 0001215075 scopus 로고
    • Explosion en temps fini pour le flot des applications harmoniques
    • Coron J.-M., Ghidaglia J.-M. Explosion en temps fini pour le flot des applications harmoniques. C. R. Acad. Sci. Paris Sér. I Math 1989, 308(12):339-344.
    • (1989) C. R. Acad. Sci. Paris Sér. I Math , vol.308 , Issue.12 , pp. 339-344
    • Coron, J.-M.1    Ghidaglia, J.-M.2
  • 51
    • 0001970571 scopus 로고
    • Minimizing p-harmonic maps into spheres
    • Coron J.-M., Gulliver R. Minimizing p-harmonic maps into spheres. J. Reine Angew. Math 1989, 401:82-100.
    • (1989) J. Reine Angew. Math , vol.401 , pp. 82-100
    • Coron, J.-M.1    Gulliver, R.2
  • 53
    • 84956209083 scopus 로고
    • Twistor spaces and harmonic maps
    • (291) (Russian)
    • Davidov I., Sergeev A.G. Twistor spaces and harmonic maps. Uspekhi Mat. Nauk 1993, 48(3):3-96. (291) (Russian).
    • (1993) Uspekhi Mat. Nauk , vol.48 , Issue.3 , pp. 3-96
    • Davidov, I.1    Sergeev, A.G.2
  • 55
    • 51249173755 scopus 로고
    • Lusternik-Schnirelman theory for harmonic maps
    • Ding W.Y. Lusternik-Schnirelman theory for harmonic maps. Acta Math. Sinica 1986, 2:15-122.
    • (1986) Acta Math. Sinica , vol.2 , pp. 15-122
    • Ding, W.Y.1
  • 56
    • 0001328886 scopus 로고
    • Symmetric harmonic maps between spheres
    • Ding W.Y. Symmetric harmonic maps between spheres. Comm. Math. Phys 1988, 118(4):641-649.
    • (1988) Comm. Math. Phys , vol.118 , Issue.4 , pp. 641-649
    • Ding, W.Y.1
  • 57
    • 0000007835 scopus 로고
    • Harmonic Hopf constructions between spheres
    • Ding W.Y. Harmonic Hopf constructions between spheres. Internat. J. Math 1994, 5(4):641-649.
    • (1994) Internat. J. Math , vol.5 , Issue.4 , pp. 641-649
    • Ding, W.Y.1
  • 59
    • 0000940315 scopus 로고
    • Energy identity for a class of approximate harmonic maps from surfaces
    • Ding W.Y., Tian G. Energy identity for a class of approximate harmonic maps from surfaces. Comm. Anal. Geom 1995, 3:543-554.
    • (1995) Comm. Anal. Geom , vol.3 , pp. 543-554
    • Ding, W.Y.1    Tian, G.2
  • 61
    • 0000072360 scopus 로고    scopus 로고
    • Weierstrass type representation of harmonic maps into symmetric spaces
    • Dorfmeister J., Pedit F., Wu H. Weierstrass type representation of harmonic maps into symmetric spaces. Comm. Anal. Geom 1998, 6(4):633-668.
    • (1998) Comm. Anal. Geom , vol.6 , Issue.4 , pp. 633-668
    • Dorfmeister, J.1    Pedit, F.2    Wu, H.3
  • 63
    • 0003335976 scopus 로고
    • Selected Topics in Harmonic Maps
    • American Mathematical Society, Providence, RI
    • Eells J., Lemaire L. Selected Topics in Harmonic Maps. C.B.M.S. Regional Conf. Series 1983, 50. American Mathematical Society, Providence, RI.
    • (1983) C.B.M.S. Regional Conf. Series , vol.50
    • Eells, J.1    Lemaire, L.2
  • 65
    • 0003320153 scopus 로고
    • Hamonic maps and minimal immersions with symmetries
    • Princeton University Press
    • Eells J., Ratto A. Hamonic maps and minimal immersions with symmetries. Annals of Math. Studies 1993, Princeton University Press.
    • (1993) Annals of Math. Studies
    • Eells, J.1    Ratto, A.2
  • 66
    • 0000818374 scopus 로고
    • Twistorial construction of harmonic maps of surfaces into four-manifolds
    • Eells J., Salamon S. Twistorial construction of harmonic maps of surfaces into four-manifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci 1985, 12(4):589-640.
    • (1985) Ann. Scuola Norm. Sup. Pisa Cl. Sci , vol.12 , Issue.4 , pp. 589-640
    • Eells, J.1    Salamon, S.2
  • 67
    • 0001675252 scopus 로고
    • Harmonic mappings of Riemannian manifolds
    • Eells J., Sampson J.H. Harmonic mappings of Riemannian manifolds. Amer. J. Math 1964, 86:109-160.
    • (1964) Amer. J. Math , vol.86 , pp. 109-160
    • Eells, J.1    Sampson, J.H.2
  • 68
    • 0000456654 scopus 로고
    • Restrictions on harmonic maps of surfaces
    • Eells J., Wood J.C. Restrictions on harmonic maps of surfaces. Topology 1976, 15:263-266.
    • (1976) Topology , vol.15 , pp. 263-266
    • Eells, J.1    Wood, J.C.2
  • 69
    • 0000610931 scopus 로고
    • Harmonic maps from surfaces to complex projective spaces
    • Eells J., Wood C. Harmonic maps from surfaces to complex projective spaces. Adv. in Math 1983, 49:217-263.
    • (1983) Adv. in Math , vol.49 , pp. 217-263
    • Eells, J.1    Wood, C.2
  • 70
    • 0032008596 scopus 로고    scopus 로고
    • Associated families of pluriharmonic maps and isotropy
    • Eschenburg J.-H., Tribuzy R. Associated families of pluriharmonic maps and isotropy. Manuscripta Math 1998, 95(3):295-310.
    • (1998) Manuscripta Math , vol.95 , Issue.3 , pp. 295-310
    • Eschenburg, J.-H.1    Tribuzy, R.2
  • 71
    • 0002104157 scopus 로고
    • Partial regularity for stationary harmonic maps into spheres
    • Evans L.C. Partial regularity for stationary harmonic maps into spheres. Arch. Rational Mech. Anal 1991, 116(2):101-113.
    • (1991) Arch. Rational Mech. Anal , vol.116 , Issue.2 , pp. 101-113
    • Evans, L.C.1
  • 72
    • 84966226124 scopus 로고
    • The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
    • Federer H. The singular sets of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension. Bull. Amer. Math. Soc 1970, 76:767-771.
    • (1970) Bull. Amer. Math. Soc , vol.76 , pp. 767-771
    • Federer, H.1
  • 73
    • 33745325637 scopus 로고
    • p spaces of several variables
    • p spaces of several variables. Acta Math 1972, 129(3-4):137-193.
    • (1972) Acta Math , vol.129 , Issue.3-4 , pp. 137-193
    • Fefferman, C.1    Stein, E.M.2
  • 74
  • 75
    • 0002992397 scopus 로고
    • Uniqueness for the harmonic map flow in two dimensions
    • Freire A. Uniqueness for the harmonic map flow in two dimensions. Calc. Var. Partial Differential Equations 1995, 3:95-105.
    • (1995) Calc. Var. Partial Differential Equations , vol.3 , pp. 95-105
    • Freire, A.1
  • 76
    • 51249165229 scopus 로고    scopus 로고
    • Uniqueness for the harmonic map flow from surfaces to general targets
    • 2) (1995) 310-338; CORRECTION IN COMMENT. MATH. HELV. 71(2
    • Freire A. Uniqueness for the harmonic map flow from surfaces to general targets. Comment. Math. Helv 1996, 70(2) (1995) 310-338; correction in Comment. Math. Helv. 71(2):330-337.
    • (1996) Comment. Math. Helv , vol.70 , pp. 330-337
    • Freire, A.1
  • 78
    • 1542681267 scopus 로고
    • P-harmonic obstacle problems II. Extensions of maps and applications
    • Fuchs M. p-harmonic obstacle problems II. Extensions of maps and applications. Manuscripta Math 1989, 63(4):381-419.
    • (1989) Manuscripta Math , vol.63 , Issue.4 , pp. 381-419
    • Fuchs, M.1
  • 79
    • 0001451390 scopus 로고
    • Harmonic morphisms between Riemannian manifolds
    • Fuglede B. Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier (Grenoble) 1978, 28(2):107-144.
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , Issue.2 , pp. 107-144
    • Fuglede, B.1
  • 80
    • 0010037411 scopus 로고    scopus 로고
    • Regularity theory for minimizing equivariant p-harmonic mappings
    • Gastel A. Regularity theory for minimizing equivariant p-harmonic mappings. Calc. Var. Partial Differential Equations 1998, 6(4):329-367.
    • (1998) Calc. Var. Partial Differential Equations , vol.6 , Issue.4 , pp. 329-367
    • Gastel, A.1
  • 81
    • 0032209345 scopus 로고    scopus 로고
    • Construction of harmonic maps between spheres by joining three eigenmaps
    • Gastel A. Construction of harmonic maps between spheres by joining three eigenmaps. Internat. J. Math 1998, 9(7):821-844.
    • (1998) Internat. J. Math , vol.9 , Issue.7 , pp. 821-844
    • Gastel, A.1
  • 82
    • 10644226012 scopus 로고    scopus 로고
    • Torus equivariant harmonic maps between spheres
    • Gastel A. Torus equivariant harmonic maps between spheres. Topology 2002, 41(2):227-231.
    • (2002) Topology , vol.41 , Issue.2 , pp. 227-231
    • Gastel, A.1
  • 83
    • 0742289028 scopus 로고    scopus 로고
    • On the harmonic Hopf construction
    • Gastel A. On the harmonic Hopf construction. Proc. Amer. Math. Soc 2004, 132(2):607-615.
    • (2004) Proc. Amer. Math. Soc , vol.132 , Issue.2 , pp. 607-615
    • Gastel, A.1
  • 84
    • 84882553557 scopus 로고    scopus 로고
    • Harmonic maps of degree 1 into the unit 2-sphere
    • Ge Y. Harmonic maps of degree 1 into the unit 2-sphere. Asian J. Math 2000, 4(3):621-632.
    • (2000) Asian J. Math , vol.4 , Issue.3 , pp. 621-632
    • Ge, Y.1
  • 86
    • 0001812542 scopus 로고
    • On the regularity of the minima of variational integrals
    • Giaquinta M., Giusti E. On the regularity of the minima of variational integrals. Acta Math 1982, 148:31-46.
    • (1982) Acta Math , vol.148 , pp. 31-46
    • Giaquinta, M.1    Giusti, E.2
  • 87
    • 0002170931 scopus 로고
    • The singular set of the minima of certain quadratic functionals
    • Giaquinta M., Giusti E. The singular set of the minima of certain quadratic functionals. Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 1984, 11(1):45-55.
    • (1984) Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) , vol.11 , Issue.1 , pp. 45-55
    • Giaquinta, M.1    Giusti, E.2
  • 88
  • 89
    • 0010999372 scopus 로고
    • The Dirichlet energy of mappings with values into the sphere
    • Giaquinta M., Modica G., Souček J. The Dirichlet energy of mappings with values into the sphere. Manuscripta Math 1989, 65:489-507.
    • (1989) Manuscripta Math , vol.65 , pp. 489-507
    • Giaquinta, M.1    Modica, G.2    Souček, J.3
  • 93
    • 0039148639 scopus 로고
    • Imbeddings and immersions in Riemannian geometry
    • (155) (Russian)
    • Gromov M.L., Rohlin V.A. Imbeddings and immersions in Riemannian geometry. Uspehi Mat. Nauk 1970, 25(5):3-62. (155) (Russian).
    • (1970) Uspehi Mat. Nauk , vol.25 , Issue.5 , pp. 3-62
    • Gromov, M.L.1    Rohlin, V.A.2
  • 95
    • 84961477580 scopus 로고
    • Regularity of weak H-surfaces
    • Grüter M. Regularity of weak H-surfaces. J. Reine Angew. Math 1981, 329:1-15.
    • (1981) J. Reine Angew. Math , vol.329 , pp. 1-15
    • Grüter, M.1
  • 96
    • 33750350408 scopus 로고    scopus 로고
    • On the existence of harmonic morphisms from certain symmetric spaces
    • Gudmundsson S., Svensson M. On the existence of harmonic morphisms from certain symmetric spaces. J. Geom. Phys 2007, 57:353-366.
    • (2007) J. Geom. Phys , vol.57 , pp. 353-366
    • Gudmundsson, S.1    Svensson, M.2
  • 97
    • 0003201917 scopus 로고    scopus 로고
    • Harmonic maps, loop groups, and integrable systems
    • Cambridge University Press, Cambridge
    • Guest M.A. Harmonic maps, loop groups, and integrable systems. London Mathematical Society Student Texts 1997, 38. Cambridge University Press, Cambridge.
    • (1997) London Mathematical Society Student Texts , vol.38
    • Guest, M.A.1
  • 100
    • 0013208296 scopus 로고    scopus 로고
    • Sobolev mappings, co-area formula and related topics
    • Sobolev Institute Press
    • Hajłasz P. Sobolev mappings, co-area formula and related topics. In: Proc. on Analysis and Geometry, Novosibirsk 2000, 227-254. Sobolev Institute Press.
    • (2000) In: Proc. on Analysis and Geometry, Novosibirsk , pp. 227-254
    • Hajłasz, P.1
  • 101
    • 84882504760 scopus 로고    scopus 로고
    • Weakly differentiable mappings between manifolds (Memoirs of the American Math. Soc., to appear)
    • P. Hajłasz, T. Iwaniec, J. Malý and J. Onninen: Weakly differentiable mappings between manifolds (Memoirs of the American Math. Soc., to appear).
    • Hajłasz, P.1    Iwaniec, T.2    Malý, J.3    Onninen, J.4
  • 104
    • 33745132173 scopus 로고    scopus 로고
    • On the weak limits of smooth maps for the Dirichlet energy between manifolds
    • Hang F.B. On the weak limits of smooth maps for the Dirichlet energy between manifolds. Comm. Anal. Geom 2005, 13(5):929-938.
    • (2005) Comm. Anal. Geom , vol.13 , Issue.5 , pp. 929-938
    • Hang, F.B.1
  • 105
    • 0346897889 scopus 로고    scopus 로고
    • Topology of Sobolev mappings
    • Hang F.B., Lin F.H. Topology of Sobolev mappings. II Acta Math 2003, 191:55-107.
    • (2003) II Acta Math , vol.191 , pp. 55-107
    • Hang, F.B.1    Lin, F.H.2
  • 106
    • 0031540281 scopus 로고    scopus 로고
    • Singularities of harmonic maps
    • Hardt R. Singularities of harmonic maps. Bull. Amer. Math. Soc 1997, 34(1):15-34.
    • (1997) Bull. Amer. Math. Soc , vol.34 , Issue.1 , pp. 15-34
    • Hardt, R.1
  • 107
    • 0000961863 scopus 로고
    • Existence and partial regularity of static liquid crystal configurations
    • Hardt R., Kinderlehrer D., Lin F.H. Existence and partial regularity of static liquid crystal configurations. Comm. Math. Phys 1986, 105:547-570.
    • (1986) Comm. Math. Phys , vol.105 , pp. 547-570
    • Hardt, R.1    Kinderlehrer, D.2    Lin, F.H.3
  • 112
    • 84990599123 scopus 로고
    • Axially symmetric harmonic maps minimizing a relaxed energy
    • Hardt R., Lin F.H., Poon C. Axially symmetric harmonic maps minimizing a relaxed energy. Comm. Pure Appl. Math 1992, 45:417-459.
    • (1992) Comm. Pure Appl. Math , vol.45 , pp. 417-459
    • Hardt, R.1    Lin, F.H.2    Poon, C.3
  • 114
    • 0000397895 scopus 로고
    • On homotopic harmonic maps
    • Hartman P. On homotopic harmonic maps. Canad. J. Math 1967, 19:673-687.
    • (1967) Canad. J. Math , vol.19 , pp. 673-687
    • Hartman, P.1
  • 115
    • 25944444222 scopus 로고
    • 3 et une variétériemannienne
    • 3 et une variétériemannienne. C. R. Acad. Sci. Paris 1989, 308:237-240.
    • (1989) C. R. Acad. Sci. Paris , vol.308 , pp. 237-240
    • Hélein, F.1
  • 116
    • 0010675712 scopus 로고
    • Régularité des applications harmoniques entre une surface et une sphère
    • Hélein F. Régularité des applications harmoniques entre une surface et une sphère. C. R. Acad. Sci. Paris 1990, 311:519-524.
    • (1990) C. R. Acad. Sci. Paris , vol.311 , pp. 519-524
    • Hélein, F.1
  • 117
    • 51249175174 scopus 로고
    • Regularity of weakly harmonic maps form a surface into a manifold with symmetries
    • Hélein F. Regularity of weakly harmonic maps form a surface into a manifold with symmetries. Manuscripta Math 1991, 70:293-318.
    • (1991) Manuscripta Math , vol.70 , pp. 293-318
    • Hélein, F.1
  • 118
    • 0013261076 scopus 로고
    • Harmonic diffeomorphisms with rotational symmetry
    • Hélein F. Harmonic diffeomorphisms with rotational symmetry. J. Reine Angew. Math 1991, 414:45-49.
    • (1991) J. Reine Angew. Math , vol.414 , pp. 45-49
    • Hélein, F.1
  • 119
    • 0000892935 scopus 로고
    • Régularité des applications harmoniques entre une surface et une variété riemannienne
    • Hélein F. Régularité des applications harmoniques entre une surface et une variété riemannienne. C. R. Acad. Sci. Paris 1991, 312:591-596.
    • (1991) C. R. Acad. Sci. Paris , vol.312 , pp. 591-596
    • Hélein, F.1
  • 120
    • 84882462369 scopus 로고    scopus 로고
    • Harmonic maps, constant mean curvature surfaces and integrable systems
    • ETH Zürich, Birkhäuser
    • Hélein F. Harmonic maps, constant mean curvature surfaces and integrable systems. Lectures in Mathematics 2001, ETH Zürich, Birkhäuser.
    • (2001) Lectures in Mathematics
    • Hélein, F.1
  • 121
    • 7244240322 scopus 로고    scopus 로고
    • Harmonic maps, conservation laws and moving frames
    • Cambridge University Press
    • Hélein F. Harmonic maps, conservation laws and moving frames. Cambridge Tracts in Mathematics 2002, 150. Cambridge University Press.
    • (2002) Cambridge Tracts in Mathematics , vol.150
    • Hélein, F.1
  • 122
    • 0038509071 scopus 로고
    • Harmonic mappings into Riemannian manifolds with non-positive sectional curvature
    • Hildebrandt S., Jäger W., Widman K.-O. Harmonic mappings into Riemannian manifolds with non-positive sectional curvature. Math. Scand 1975, 37(2):257-263.
    • (1975) Math. Scand , vol.37 , Issue.2 , pp. 257-263
    • Hildebrandt, S.1    Jäger, W.2    Widman, K.-O.3
  • 123
    • 0002442550 scopus 로고
    • An existence theorem for harmonic mappings of Riemannian manifolds
    • Hildebrandt S., Jäger W., Widman K.-O. An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math 1977, 138(1-2):1-16.
    • (1977) Acta Math , vol.138 , Issue.1-2 , pp. 1-16
    • Hildebrandt, S.1    Jäger, W.2    Widman, K.-O.3
  • 124
    • 0011663530 scopus 로고
    • On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order
    • Hildebrandt S., Widman K.-O. On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 1977, 4(1):145-178.
    • (1977) Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) , vol.4 , Issue.1 , pp. 145-178
    • Hildebrandt, S.1    Widman, K.-O.2
  • 125
    • 84972507643 scopus 로고
    • Harmonic maps from a 2-torus to a 3-sphere
    • Hitchin N. Harmonic maps from a 2-torus to a 3-sphere. J. Diff. Geom 1990, 31:627-710.
    • (1990) J. Diff. Geom , vol.31 , pp. 627-710
    • Hitchin, N.1
  • 127
    • 0000430059 scopus 로고
    • A mapping of Riemannian manifolds which preserves harmonic functions
    • Ishihara T. A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Kyoto Univ 1979, 19:215-229.
    • (1979) J. Math. Kyoto Univ , vol.19 , pp. 215-229
    • Ishihara, T.1
  • 129
    • 0002943709 scopus 로고
    • Uniqueness and stability of harmonic maps and their Jacobi fields
    • Jäger W., Kaul H. Uniqueness and stability of harmonic maps and their Jacobi fields. Manuscripta Math 1979, 28:269-291.
    • (1979) Manuscripta Math , vol.28 , pp. 269-291
    • Jäger, W.1    Kaul, H.2
  • 130
    • 0000225382 scopus 로고
    • Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems
    • Jäger W., Kaul H. Rotationally symmetric harmonic maps from a ball into a sphere and the regularity problem for weak solutions of elliptic systems. J. Reine Angew. Math 1983, 343:146-161.
    • (1983) J. Reine Angew. Math , vol.343 , pp. 146-161
    • Jäger, W.1    Kaul, H.2
  • 131
    • 84980082306 scopus 로고
    • On functions of bounded mean oscillation
    • John F., Nirenberg L. On functions of bounded mean oscillation. Comm. Pure and Appl. Math 1961, 14:415-426.
    • (1961) Comm. Pure and Appl. Math , vol.14 , pp. 415-426
    • John, F.1    Nirenberg, L.2
  • 132
    • 34250224179 scopus 로고
    • A maximum principle for harmonic mappings which solves a Dirichlet problem
    • Jost J. A maximum principle for harmonic mappings which solves a Dirichlet problem. Manuscripta Math 1982, 38:129-130.
    • (1982) Manuscripta Math , vol.38 , pp. 129-130
    • Jost, J.1
  • 133
    • 34250148749 scopus 로고
    • Existence proof for harmonic mappings with the help of the maximum principle
    • Jost J. Existence proof for harmonic mappings with the help of the maximum principle. Math. Z 1983, 184:489-496.
    • (1983) Math. Z , vol.184 , pp. 489-496
    • Jost, J.1
  • 134
    • 84972525390 scopus 로고
    • The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values
    • Jost J. The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values. J. Diff. Geom 1984, 19(2):393-401.
    • (1984) J. Diff. Geom , vol.19 , Issue.2 , pp. 393-401
    • Jost, J.1
  • 139
    • 67649670889 scopus 로고
    • Almost linear functions and a priori estimates for harmonic maps
    • Durham, 1982, E. Horwood, Chichester
    • Jost J., Karcher H. Almost linear functions and a priori estimates for harmonic maps. In: Global Riemmannian Geometry 1984, 148-155. Durham, 1982, E. Horwood, Chichester.
    • (1984) In: Global Riemmannian Geometry , pp. 148-155
    • Jost, J.1    Karcher, H.2
  • 140
    • 0003172342 scopus 로고
    • On the existence of harmonic diffeomorphisms
    • Jost J., Schoen R. On the existence of harmonic diffeomorphisms. Invent. Math 1982, 66(2):353-359.
    • (1982) Invent. Math , vol.66 , Issue.2 , pp. 353-359
    • Jost, J.1    Schoen, R.2
  • 141
    • 0041135109 scopus 로고
    • Morse-Conley theory for minimal surfaces of varying topological type
    • Jost J., Struwe M. Morse-Conley theory for minimal surfaces of varying topological type. Invent. Math 1990, 102(3):465-499.
    • (1990) Invent. Math , vol.102 , Issue.3 , pp. 465-499
    • Jost, J.1    Struwe, M.2
  • 142
    • 0000119732 scopus 로고
    • Complete constant mean curvature surfaces in Euclidean three-space
    • Kapouleas N. Complete constant mean curvature surfaces in Euclidean three-space. Ann. of Math., (2) 1990, 131(2):239-330.
    • (1990) Ann. of Math., (2) , vol.131 , Issue.2 , pp. 239-330
    • Kapouleas, N.1
  • 143
    • 84972514262 scopus 로고
    • Compact constant mean curvature surfaces in Euclidean three-space
    • Kapouleas N. Compact constant mean curvature surfaces in Euclidean three-space. J. Diff. Geom 1991, 33(3):683-715.
    • (1991) J. Diff. Geom , vol.33 , Issue.3 , pp. 683-715
    • Kapouleas, N.1
  • 144
    • 0001494078 scopus 로고
    • Constant mean curvature surfaces constructed by fusing Wente tori
    • Kapouleas N. Constant mean curvature surfaces constructed by fusing Wente tori. Invent. Math 1995, 119(3):443-518.
    • (1995) Invent. Math , vol.119 , Issue.3 , pp. 443-518
    • Kapouleas, N.1
  • 145
    • 0001678677 scopus 로고
    • Non-existence results and growth properties for harmonic maps and forms
    • Karcher H., Wood J.C. Non-existence results and growth properties for harmonic maps and forms. J. Reine Angew. Math 1984, 353:165-180.
    • (1984) J. Reine Angew. Math , vol.353 , pp. 165-180
    • Karcher, H.1    Wood, J.C.2
  • 146
    • 51249161862 scopus 로고
    • Minimizing the energy from a surface into a 2-sphere with prescribed degree and boundary values
    • Kuwert E. Minimizing the energy from a surface into a 2-sphere with prescribed degree and boundary values. Manuscripta Math 1994, 83:31-38.
    • (1994) Manuscripta Math , vol.83 , pp. 31-38
    • Kuwert, E.1
  • 148
    • 0002009569 scopus 로고
    • Applications harmoniques de surfaces riemanniennes
    • Lemaire L. Applications harmoniques de surfaces riemanniennes. J. Diff. Geom. 1979, 13:51-78.
    • (1979) J. Diff. Geom. , vol.13 , pp. 51-78
    • Lemaire, L.1
  • 152
    • 0006848881 scopus 로고
    • A remark on the map x/|x|
    • Lin F.H. A remark on the map x/|x|. C. R. Acad. Sci. Paris 1987, 305:529-531.
    • (1987) C. R. Acad. Sci. Paris , vol.305 , pp. 529-531
    • Lin, F.H.1
  • 153
    • 0033470202 scopus 로고    scopus 로고
    • Gradient estimates and blow-up analysis for stationary harmonic maps
    • Lin F.H. Gradient estimates and blow-up analysis for stationary harmonic maps. Ann. of Math., (2) 1999, 149(3):785-829.
    • (1999) Ann. of Math., (2) , vol.149 , Issue.3 , pp. 785-829
    • Lin, F.H.1
  • 155
    • 0037082240 scopus 로고    scopus 로고
    • Energy quantization for harmonic maps
    • Lin F.H., Rivière T. Energy quantization for harmonic maps. Duke Math. J 2002, 111(1):177-193.
    • (2002) Duke Math. J , vol.111 , Issue.1 , pp. 177-193
    • Lin, F.H.1    Rivière, T.2
  • 156
    • 0001294182 scopus 로고
    • The concentration-compactness principle in the calculus of variations
    • Lions P.-L. The concentration-compactness principle in the calculus of variations. The limit case I and II Rev. Mat. Iberoamericana 1985, 1(1):145-201.
    • (1985) The limit case I and II Rev. Mat. Iberoamericana , vol.1 , Issue.1 , pp. 145-201
    • Lions, P.-L.1
  • 158
    • 0001221762 scopus 로고
    • Partial Hölder continuity for minima of certain energies among maps into a Riemannian manifold
    • Luckhaus S. Partial Hölder continuity for minima of certain energies among maps into a Riemannian manifold. Indiana Univ. Math. J 1988, 37(2):349-367.
    • (1988) Indiana Univ. Math. J , vol.37 , Issue.2 , pp. 349-367
    • Luckhaus, S.1
  • 159
    • 0000376473 scopus 로고
    • Convergence of minimizers for the p-Dirichlet integral
    • Luckhaus S. Convergence of minimizers for the p-Dirichlet integral. Math. Z 1993, 213:449-456.
    • (1993) Math. Z , vol.213 , pp. 449-456
    • Luckhaus, S.1
  • 160
    • 0035638786 scopus 로고    scopus 로고
    • Connected sums of constant mean curvature surfaces in Euclidean 3 space
    • Mazzeo R., Pacard F. Connected sums of constant mean curvature surfaces in Euclidean 3 space. J. Reine Angew. Math 2001, 536:115-165.
    • (2001) J. Reine Angew. Math , vol.536 , pp. 115-165
    • Mazzeo, R.1    Pacard, F.2
  • 162
    • 84882467517 scopus 로고    scopus 로고
    • 1-valued fractional Sobolev spaces
    • 1-valued fractional Sobolev spaces. Contemporary Math 2004, 350:201-207.
    • (2004) Contemporary Math , vol.350 , pp. 201-207
    • Mironescu, P.1
  • 163
    • 0000235872 scopus 로고
    • The problem of Plateau on a Riemannian manifold
    • Morrey C.B. The problem of Plateau on a Riemannian manifold. Annals of Math 1948, 49(4):807-851.
    • (1948) Annals of Math , vol.49 , Issue.4 , pp. 807-851
    • Morrey, C.B.1
  • 165
    • 8744225639 scopus 로고    scopus 로고
    • Regularity of n-harmonic maps
    • Mou L., Yang P. Regularity of n-harmonic maps. J. Geom. Anal 1996, 6(1):91-112.
    • (1996) J. Geom. Anal , vol.6 , Issue.1 , pp. 91-112
    • Mou, L.1    Yang, P.2
  • 166
    • 0000485374 scopus 로고
    • Compacité par compensation: condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant
    • Murat F. Compacité par compensation: condition nécessaire et suffisante de continuité faible sous une hypothèse de rang constant. Ann. Scuola Normale Sup., Pisa, Serie VIII 1981, 1:69-102.
    • (1981) Ann. Scuola Normale Sup., Pisa, Serie VIII , vol.1 , pp. 69-102
    • Murat, F.1
  • 168
    • 33746742950 scopus 로고    scopus 로고
    • Twistor fibrations giving primitive harmonic maps of finite type
    • Pacheco R. Twistor fibrations giving primitive harmonic maps of finite type. Int. J. Math. Math. Sci 2005, 20:3199-3212.
    • (2005) Int. J. Math. Math. Sci , vol.20 , pp. 3199-3212
    • Pacheco, R.1
  • 169
    • 0037562160 scopus 로고    scopus 로고
    • Weak density of smooth maps for the Dirichlet energy between manifolds
    • Pakzad M.R., Rivière T. Weak density of smooth maps for the Dirichlet energy between manifolds. Geom. Funct. Anal 2003, 13(1):223-257.
    • (2003) Geom. Funct. Anal , vol.13 , Issue.1 , pp. 223-257
    • Pakzad, M.R.1    Rivière, T.2
  • 170
    • 0002783768 scopus 로고
    • The principle of symmetric criticality
    • Palais R. The principle of symmetric criticality. Comm. Math. Phys 1979, 69(1):19-30.
    • (1979) Comm. Math. Phys , vol.69 , Issue.1 , pp. 19-30
    • Palais, R.1
  • 171
    • 0030267775 scopus 로고    scopus 로고
    • Bubble tree convergence for harmonic maps
    • Parker T.H. Bubble tree convergence for harmonic maps. J. Diff. Geom 1996, 44(3):595-633.
    • (1996) J. Diff. Geom , vol.44 , Issue.3 , pp. 595-633
    • Parker, T.H.1
  • 172
    • 0003097109 scopus 로고
    • Solutions of the zero rest-mass equations
    • Penrose R. Solutions of the zero rest-mass equations. J. Math. Phys 1969, 10:38-39.
    • (1969) J. Math. Phys , vol.10 , pp. 38-39
    • Penrose, R.1
  • 173
    • 0001905459 scopus 로고
    • Eine neue Behandlung der ersten Randwertaufgabe für Δu = 0
    • Perron O. Eine neue Behandlung der ersten Randwertaufgabe für Δu = 0. Math. Z 1923, 18:42-54.
    • (1923) Math. Z , vol.18 , pp. 42-54
    • Perron, O.1
  • 174
    • 0001591942 scopus 로고
    • Existence and non-existence results for harmonic maps between spheres
    • Pettinati V., Ratto A. Existence and non-existence results for harmonic maps between spheres. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 1991, 17(2):273-282.
    • (1991) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.17 , Issue.2 , pp. 273-282
    • Pettinati, V.1    Ratto, A.2
  • 175
    • 0039291545 scopus 로고
    • Sur l'analyticité des solutions des systèmes d'équations différentielles
    • Petrowsky I.G. Sur l'analyticité des solutions des systèmes d'équations différentielles. Rec. Math. (N. S.) [Mat. Sbornik], (5) 1939, 47:3-70.
    • (1939) Rec. Math. (N. S.) [Mat. Sbornik], (5) , vol.47 , pp. 3-70
    • Petrowsky, I.G.1
  • 176
    • 0000784824 scopus 로고
    • On the classification of constant mean curvature tori
    • Pinkall U., Sterling I. On the classification of constant mean curvature tori. Ann. Math 1989, 130:407-451.
    • (1989) Ann. Math , vol.130 , pp. 407-451
    • Pinkall, U.1    Sterling, I.2
  • 177
    • 0038753820 scopus 로고
    • Some properties of harmonic mappings in the case of spheres and Lie groups
    • Pluzhnikov A.I. Some properties of harmonic mappings in the case of spheres and Lie groups. Sov. Math. Dokl 1983, 27:246-248.
    • (1983) Sov. Math. Dokl , vol.27 , pp. 246-248
    • Pluzhnikov, A.I.1
  • 178
    • 84882489468 scopus 로고
    • A topological criterion for the attainability of global minima of an energy function
    • Pluzhnikov A.I. A topological criterion for the attainability of global minima of an energy function. Nov. Glob. Anal. Voronezh. Gos. Univ 1986, 177:149-155.
    • (1986) Nov. Glob. Anal. Voronezh. Gos. Univ , vol.177 , pp. 149-155
    • Pluzhnikov, A.I.1
  • 179
    • 34250385489 scopus 로고
    • Integrable Hamiltonian systems and interactions through constraints
    • Pohlmeyer K. Integrable Hamiltonian systems and interactions through constraints. Comm. Math. Phys 1976, 46:207-221.
    • (1976) Comm. Math. Phys , vol.46 , pp. 207-221
    • Pohlmeyer, K.1
  • 180
    • 0000323549 scopus 로고
    • Sur les équations aux dérivées partielles de la physique mathématique
    • Poincaré H. Sur les équations aux dérivées partielles de la physique mathématique. Amer. J. Math 1890, 12:211-294.
    • (1890) Amer. J. Math , vol.12 , pp. 211-294
    • Poincaré, H.1
  • 181
    • 3142555528 scopus 로고
    • Remark on the Dirichlet problem for harmonic maps from the disc into the 2-sphere
    • Qing J. Remark on the Dirichlet problem for harmonic maps from the disc into the 2-sphere. Proc. Roy. Soc. Edinburgh 1992, 122A:63-67.
    • (1992) Proc. Roy. Soc. Edinburgh , vol.122 A , pp. 63-67
    • Qing, J.1
  • 182
    • 51249163520 scopus 로고
    • Multiple solutions of the Dirichlet problem for harmonic maps from discs into 2-spheres
    • Qing J. Multiple solutions of the Dirichlet problem for harmonic maps from discs into 2-spheres. Manuscripta Math 1992, 77(4):435-446.
    • (1992) Manuscripta Math , vol.77 , Issue.4 , pp. 435-446
    • Qing, J.1
  • 183
    • 84962999159 scopus 로고
    • The Dirichlet problem for harmonic maps from the disc into Kähler manifolds
    • Qing J. The Dirichlet problem for harmonic maps from the disc into Kähler manifolds. J. London Math. Soc., (2) 1993, 47(1):182-192.
    • (1993) J. London Math. Soc., (2) , vol.47 , Issue.1 , pp. 182-192
    • Qing, J.1
  • 184
    • 0001102614 scopus 로고
    • On the singularities of the heat flow for harmonic maps from surfaces into spheres
    • Qing J. On the singularities of the heat flow for harmonic maps from surfaces into spheres. Comm. Anal. Geom 1995, 3(1-2):297-315.
    • (1995) Comm. Anal. Geom , vol.3 , Issue.1-2 , pp. 297-315
    • Qing, J.1
  • 185
    • 0031481224 scopus 로고    scopus 로고
    • Bubbling of the heat flows for harmonic maps from surface
    • Qing J., Tian G. Bubbling of the heat flows for harmonic maps from surface. Comm. Pure Appl. Math 1997, 50:295-310.
    • (1997) Comm. Pure Appl. Math , vol.50 , pp. 295-310
    • Qing, J.1    Tian, G.2
  • 186
    • 38249021642 scopus 로고
    • Harmonic maps of spheres and the Hopf construction
    • Ratto A. Harmonic maps of spheres and the Hopf construction. Topology 1989, 28(3):379-388.
    • (1989) Topology , vol.28 , Issue.3 , pp. 379-388
    • Ratto, A.1
  • 187
    • 0010114905 scopus 로고
    • F-structures, f-twistor spaces and harmonic maps
    • Springer, Berlin, Heidelberg, New York, Lect. Notes Math, L. Bianchi (Ed.)
    • Rawnsley J.H. f-structures, f-twistor spaces and harmonic maps. In: Geometry Seminar 1985, 1164:85-159. Springer, Berlin, Heidelberg, New York, Lect. Notes Math. L. Bianchi (Ed.).
    • (1985) In: Geometry Seminar , vol.1164 , pp. 85-159
    • Rawnsley, J.H.1
  • 189
    • 0000301066 scopus 로고
    • Everywhere discontinuous harmonic maps into spheres
    • Rivière T. Everywhere discontinuous harmonic maps into spheres. Acta Math 1995, 175:197-226.
    • (1995) Acta Math , vol.175 , pp. 197-226
    • Rivière, T.1
  • 191
    • 33847320537 scopus 로고    scopus 로고
    • Conservation laws for conformally invariant variational problems
    • Rivière T. Conservation laws for conformally invariant variational problems. Invent. Math 2007, 168(1):1-22.
    • (2007) Invent. Math , vol.168 , Issue.1 , pp. 1-22
    • Rivière, T.1
  • 192
    • 84882462754 scopus 로고    scopus 로고
    • Partial regularity for harmonic maps, and related problems
    • Rivière T., Struwe M. Partial regularity for harmonic maps, and related problems. Preprint 2006.
    • (2006) Preprint
    • Rivière, T.1    Struwe, M.2
  • 193
    • 0030547974 scopus 로고    scopus 로고
    • Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents
    • Rubinstein J., Sternberg P. Homotopy classification of minimizers of the Ginzburg-Landau energy and the existence of permanent currents. Comm. Math. Phys 1996, 179:257-263.
    • (1996) Comm. Math. Phys , vol.179 , pp. 257-263
    • Rubinstein, J.1    Sternberg, P.2
  • 194
    • 0000789799 scopus 로고
    • The tension field of the Gauss map
    • Ruh E.A., Vilms J. The tension field of the Gauss map. Trans. Amer. Math. Soc 1970, 149:569-573.
    • (1970) Trans. Amer. Math. Soc , vol.149 , pp. 569-573
    • Ruh, E.A.1    Vilms, J.2
  • 195
    • 67650819302 scopus 로고
    • The existence of minimal immersions of two-spheres
    • Sacks J., Uhlenbeck K. The existence of minimal immersions of two-spheres. Bull. Amer. Math. Soc 1977, 83:1033-1036.
    • (1977) Bull. Amer. Math. Soc , vol.83 , pp. 1033-1036
    • Sacks, J.1    Uhlenbeck, K.2
  • 196
    • 0002957091 scopus 로고
    • The existence of minimal immersions of 2-spheres
    • Sacks J., Uhlenbeck K. The existence of minimal immersions of 2-spheres. Ann. Math., (2) 1981, 113:1-24.
    • (1981) Ann. Math., (2) , vol.113 , pp. 1-24
    • Sacks, J.1    Uhlenbeck, K.2
  • 197
    • 0002530417 scopus 로고
    • Analytic aspects of the harmonic maps problem
    • Springer, S.S. Chern (Ed.)
    • Schoen R. Analytic aspects of the harmonic maps problem. In: Seminar on nonlinear PDE 1984, 321-358. Springer. (ed.). S.S. Chern (Ed.).
    • (1984) In: Seminar on nonlinear PDE , pp. 321-358
    • Schoen, R.1
  • 198
    • 84972544463 scopus 로고
    • A regularity theory for harmonic maps
    • Schoen R., Uhlenbeck K. A regularity theory for harmonic maps. J. Diff. Geom 1982, 17:307-335.
    • (1982) J. Diff. Geom , vol.17 , pp. 307-335
    • Schoen, R.1    Uhlenbeck, K.2
  • 199
    • 84972525916 scopus 로고
    • Boundary regularity and the Dirichlet problem for harmonic maps
    • Schoen R., Uhlenbeck K. Boundary regularity and the Dirichlet problem for harmonic maps. J. Diff. Geom 1983, 18:253-268.
    • (1983) J. Diff. Geom , vol.18 , pp. 253-268
    • Schoen, R.1    Uhlenbeck, K.2
  • 200
    • 0002260833 scopus 로고
    • Regularity of minimizing harmonic maps into the sphere
    • Schoen R., Uhlenbeck K. Regularity of minimizing harmonic maps into the sphere. Invent. Math 1984, 78(1):89-100.
    • (1984) Invent. Math , vol.78 , Issue.1 , pp. 89-100
    • Schoen, R.1    Uhlenbeck, K.2
  • 201
    • 0001593830 scopus 로고
    • Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature
    • Schoen R., Yau S.T. Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature. Ann. of Math 1979, 110:127-142.
    • (1979) Ann. of Math , vol.110 , pp. 127-142
    • Schoen, R.1    Yau, S.T.2
  • 203
    • 0004100833 scopus 로고    scopus 로고
    • Hermann, Paris Nouveau tirage, 1st edn., (1950/1951)
    • Schwartz L. Théorie des Distributions 1998, Hermann, Paris Nouveau tirage, 1st edn., (1950/1951).
    • (1998) Théorie des Distributions
    • Schwartz, L.1
  • 205
    • 84990623256 scopus 로고
    • Weak solutions and developments of singularities of the SU(2) σ-model
    • Shatah J. Weak solutions and developments of singularities of the SU(2) σ-model. Comm. Pure Appl. Math 1988, 41:459-469.
    • (1988) Comm. Pure Appl. Math , vol.41 , pp. 459-469
    • Shatah, J.1
  • 206
    • 0000137102 scopus 로고
    • Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems
    • Simon L. Asymptotics for a class of nonlinear evolution equations, with applications to geometric problems. Ann. of Math., (2) 1983, 118(3):525-571.
    • (1983) Ann. of Math., (2) , vol.118 , Issue.3 , pp. 525-571
    • Simon, L.1
  • 207
    • 0039461839 scopus 로고
    • Theorems on the regularity and singularity of minimal surfaces and harmonic maps
    • Tohoku Univ., Sendai
    • Simon L. Theorems on the regularity and singularity of minimal surfaces and harmonic maps. In: Geometry and Global Analysis 1993, 111-145. Tohoku Univ., Sendai.
    • (1993) In: Geometry and Global Analysis , pp. 111-145
    • Simon, L.1
  • 208
    • 0003374625 scopus 로고
    • Rectifiability of the singular set of energy minimizing maps
    • Simon L. Rectifiability of the singular set of energy minimizing maps. Calc. Var. Partial Differential Equations 1995, 3:1-65.
    • (1995) Calc. Var. Partial Differential Equations , vol.3 , pp. 1-65
    • Simon, L.1
  • 209
    • 0040294916 scopus 로고    scopus 로고
    • Theorems on regularity and singularity of energy minimizing maps
    • ETH Zürich, Birkhäuser
    • Simon L. Theorems on regularity and singularity of energy minimizing maps. Lectures in Mathematics 1996, ETH Zürich, Birkhäuser.
    • (1996) Lectures in Mathematics
    • Simon, L.1
  • 210
    • 0000765708 scopus 로고
    • Harmonic mappings of spheres
    • Smith R.T. Harmonic mappings of spheres. Amer. J. Math 1975, 97:364-385.
    • (1975) Amer. J. Math , vol.97 , pp. 364-385
    • Smith, R.T.1
  • 211
    • 84971168534 scopus 로고
    • The Dirichlet problem for harmonic maps from the disc into the 2-sphere
    • Soyeur A. The Dirichlet problem for harmonic maps from the disc into the 2-sphere. Proc. Royal Soc. Edinburgh 1989, 113A:229-234.
    • (1989) Proc. Royal Soc. Edinburgh , vol.113 A , pp. 229-234
    • Soyeur, A.1
  • 212
  • 213
    • 0004136765 scopus 로고
    • Princeton University Press, Princeton
    • Stein E. Harmonic analysis 1993, Princeton University Press, Princeton.
    • (1993) Harmonic analysis
    • Stein, E.1
  • 215
    • 51249177065 scopus 로고
    • On the evolution of harmonic maps of Riemannian manifolds
    • Struwe M. On the evolution of harmonic maps of Riemannian manifolds. Comment. Math. Helv 1985, 60:558-581.
    • (1985) Comment. Math. Helv , vol.60 , pp. 558-581
    • Struwe, M.1
  • 216
    • 84972503995 scopus 로고
    • On the evolution of harmonic maps in higher dimensions
    • Struwe M. On the evolution of harmonic maps in higher dimensions. J. Diff. Geom 1988, 28(2):485-502.
    • (1988) J. Diff. Geom , vol.28 , Issue.2 , pp. 485-502
    • Struwe, M.1
  • 218
    • 0032129295 scopus 로고    scopus 로고
    • Uniqueness of harmonic maps with small energy
    • Struwe M. Uniqueness of harmonic maps with small energy. Manuscripta Math 1998, 96(4):463-486.
    • (1998) Manuscripta Math , vol.96 , Issue.4 , pp. 463-486
    • Struwe, M.1
  • 219
    • 0002851015 scopus 로고
    • The compensated compactness method applied to systems of conservation laws
    • NATO ASI Series C111, Reidel, New York, J.M. Ball (Ed.)
    • Tartar L. The compensated compactness method applied to systems of conservation laws. In: Systems of nonlinear partial differential equations 1983, 263-285. NATO ASI Series C111, Reidel, New York. ed. J.M. Ball (Ed.).
    • (1983) In: Systems of nonlinear partial differential equations , pp. 263-285
    • Tartar, L.1
  • 222
    • 0031089307 scopus 로고    scopus 로고
    • Rigidity of the harmonic map heat flow
    • Topping P. Rigidity of the harmonic map heat flow. J. Diff. Geom 1997, 45(3):593-610.
    • (1997) J. Diff. Geom , vol.45 , Issue.3 , pp. 593-610
    • Topping, P.1
  • 223
    • 0036350765 scopus 로고    scopus 로고
    • Reverse bubbling and nonuniqueness in the harmonic map flow
    • Topping P. Reverse bubbling and nonuniqueness in the harmonic map flow. Int. Math. Res. Not 2002, 10:505-520.
    • (2002) Int. Math. Res. Not , vol.10 , pp. 505-520
    • Topping, P.1
  • 224
    • 4644221893 scopus 로고    scopus 로고
    • Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic maps flow
    • Topping P. Repulsion and quantization in almost-harmonic maps, and asymptotics of the harmonic maps flow. Ann. of Math., (2) 2004, 159(2):465-534.
    • (2004) Ann. of Math., (2) , vol.159 , Issue.2 , pp. 465-534
    • Topping, P.1
  • 225
    • 0002529613 scopus 로고
    • Harmonic maps a direct method in the calculus of variations
    • Uhlenbeck K. Harmonic maps a direct method in the calculus of variations. Bull. Amer. Math. Soc 1970, 76:1082-1087.
    • (1970) Bull. Amer. Math. Soc , vol.76 , pp. 1082-1087
    • Uhlenbeck, K.1
  • 226
    • 34250242066 scopus 로고
    • Connections with Lp bounds on curvature
    • Uhlenbeck K. Connections with Lp bounds on curvature. Comm. Math. Phys 1982, 83(1):31-42.
    • (1982) Comm. Math. Phys , vol.83 , Issue.1 , pp. 31-42
    • Uhlenbeck, K.1
  • 227
    • 84972545531 scopus 로고
    • Harmonic maps into Lie groups classical solutions of the chiral model
    • Uhlenbeck K. Harmonic maps into Lie groups classical solutions of the chiral model. J. Diff. Geom 1989, 30(1):1-50.
    • (1989) J. Diff. Geom , vol.30 , Issue.1 , pp. 1-50
    • Uhlenbeck, K.1
  • 228
    • 0003226423 scopus 로고
    • Calculus of variations and harmonic maps
    • American Mathematical Society, Providence, RI
    • Urakawa H. Calculus of variations and harmonic maps. Translations of Mathematical Monographs 1993, 132. American Mathematical Society, Providence, RI.
    • (1993) Translations of Mathematical Monographs , vol.132
    • Urakawa, H.1
  • 229
    • 0010081220 scopus 로고
    • Harmonic maps from a closed surface of higher genus to the unit 2-sphere
    • Wang G.F. Harmonic maps from a closed surface of higher genus to the unit 2-sphere. Internat. J. Math 1993, 4:359-365.
    • (1993) Internat. J. Math , vol.4 , pp. 359-365
    • Wang, G.F.1
  • 230
    • 0001585852 scopus 로고
    • An existence theorem for surfaces of constant mean curvature
    • Wente H. An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl 1969, 26:318-344.
    • (1969) J. Math. Anal. Appl , vol.26 , pp. 318-344
    • Wente, H.1
  • 231
    • 84972553986 scopus 로고
    • Counterexample to a conjecture of H. Hopf
    • Wente H. Counterexample to a conjecture of H. Hopf. Pacific J. Math 1986, 121(1):193-243.
    • (1986) Pacific J. Math , vol.121 , Issue.1 , pp. 193-243
    • Wente, H.1
  • 232
    • 84967491274 scopus 로고
    • The method of orthogonal projection in potential theory
    • Weyl H. The method of orthogonal projection in potential theory. Duke Math. J 1940, 7:411-440.
    • (1940) Duke Math. J , vol.7 , pp. 411-440
    • Weyl, H.1
  • 234
    • 84968481696 scopus 로고
    • Homotopy classes in Sobolev spaces and energy minimizing maps
    • White B. Homotopy classes in Sobolev spaces and energy minimizing maps. Bull. Amer. Math. Soc 1986, 13:166-168.
    • (1986) Bull. Amer. Math. Soc , vol.13 , pp. 166-168
    • White, B.1
  • 235
    • 84972494609 scopus 로고
    • Infima of energy functions in homotopy classes of mappings
    • White B. Infima of energy functions in homotopy classes of mappings. J. Diff. Geom 1986, 23:127-142.
    • (1986) J. Diff. Geom , vol.23 , pp. 127-142
    • White, B.1
  • 236
    • 0002146522 scopus 로고
    • Homotopy classes in Sobolev spaces and the existence of energy minimizing maps
    • White B. Homotopy classes in Sobolev spaces and the existence of energy minimizing maps. Acta Math 1988, 160:1-17.
    • (1988) Acta Math , vol.160 , pp. 1-17
    • White, B.1
  • 237
    • 84967707827 scopus 로고
    • Nonunique tangent maps at isolated singularities of harmonic maps
    • White B. Nonunique tangent maps at isolated singularities of harmonic maps. Bull. Amer. Math. Soc 1992, 26(1):125-129.
    • (1992) Bull. Amer. Math. Soc , vol.26 , Issue.1 , pp. 125-129
    • White, B.1
  • 238
    • 0011549124 scopus 로고
    • Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer
    • Wiegner M. Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer. Systeme Math. Z 1976, 147:21-28.
    • (1976) Systeme Math. Z , vol.147 , pp. 21-28
    • Wiegner, M.1
  • 239
    • 84882461267 scopus 로고
    • Non-existence of solutions to certain Dirichlet problems for harmonic maps
    • Wood J.C. Non-existence of solutions to certain Dirichlet problems for harmonic maps. Preprint University of Leeds 1981.
    • (1981) Preprint University of Leeds
    • Wood, J.C.1


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