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Volumn 56, Issue 8, 2003, Pages 1135-1150

The Inequality of Moser and Trudinger and Applications to Conformal Geometry

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EID: 0037660833     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpa.3029     Document Type: Article
Times cited : (91)

References (56)
  • 1
    • 0000968678 scopus 로고
    • A sharp inequality of J. Moser for higher order derivatives
    • Adams, D. R. A sharp inequality of J. Moser for higher order derivatives. Ann. of Math. (2) 128 (1988), no. 2, 385-398.
    • (1988) Ann. of Math. (2) , vol.128 , Issue.2 , pp. 385-398
    • Adams, D.R.1
  • 2
    • 0000461632 scopus 로고
    • Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire
    • Aubin, T. Meilleures constantes dans le théorème d'inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire. J. Funct. Anal. 32 (1979), no. 2, 148-174.
    • (1979) J. Funct. Anal. , vol.32 , Issue.2 , pp. 148-174
    • Aubin, T.1
  • 4
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
    • Beckner, W. Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality. Ann. of Math. (2) 138 (1993), no. 1, 213-242.
    • (1993) Ann. of Math. (2) , vol.138 , Issue.1 , pp. 213-242
    • Beckner, W.1
  • 5
    • 2442441215 scopus 로고
    • Lecture Notes Series, 4. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul
    • Branson, T. P. The functional determinant. Lecture Notes Series, 4. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1993.
    • (1993) The Functional Determinant
    • Branson, T.P.1
  • 6
    • 21144476884 scopus 로고
    • Estimates and extremals for zeta function determinants on four-manifolds
    • Branson, T. P.; Chang, S.-Y. A.; Yang, Paul C. Estimates and extremals for zeta function determinants on four-manifolds. Comm. Math. Phys. 149 (1992), no. 2, 241-262.
    • (1992) Comm. Math. Phys. , vol.149 , Issue.2 , pp. 241-262
    • Branson, T.P.1    Chang, S.-Y.A.2    Yang, P.C.3
  • 7
    • 21844506740 scopus 로고
    • Vortex condensation in the Chern-Simons Higgs model: An existence theorem
    • Caffarelli, L. A.; Yang, Y. Vortex condensation in the Chern-Simons Higgs model: an existence theorem. Comm. Math. Phys. 168 (1995), no. 2, 321-336.
    • (1995) Comm. Math. Phys. , vol.168 , Issue.2 , pp. 321-336
    • Caffarelli, L.A.1    Yang, Y.2
  • 8
    • 0001611867 scopus 로고
    • On the existence of an extremal function for an inequality of J. Moser
    • Carleson, L.; Chang, S.-Y. A. On the existence of an extremal function for an inequality of J. Moser. Bull. Sci. Math. (2) 110 (1986), no. 2, 113-127.
    • (1986) Bull. Sci. Math. (2) , vol.110 , Issue.2 , pp. 113-127
    • Carleson, L.1    Chang, S.-Y.A.2
  • 9
    • 0001903711 scopus 로고
    • On Nirenberg's problem
    • Chang, K. C.; Liu, J. Q. On Nirenberg's problem. Internat. J. Math. 4 (1993), no. 1, 35-58.
    • (1993) Internat. J. Math. , vol.4 , Issue.1 , pp. 35-58
    • Chang, K.C.1    Liu, J.Q.2
  • 10
    • 2442569048 scopus 로고    scopus 로고
    • The Moser Trudinger inequality and applications to some problems in conformal geometry
    • IAS/Park City Mathematics Series, 2. American Mathematics Society, Providence, R.I.
    • Chang, S.-Y. A. The Moser Trudinger inequality and applications to some problems in conformal geometry. Nonlinear partial differential equations in differential geometry (Park City, UT, 1992), 65-125. IAS/Park City Mathematics Series, 2. American Mathematics Society, Providence, R.I., 1996.
    • (1996) Nonlinear Partial Differential Equations in Differential Geometry (Park City, UT, 1992) , pp. 65-125
    • Chang, S.-Y.A.1
  • 12
    • 0036433621 scopus 로고    scopus 로고
    • An a priori estimate for a fully nonlinear equation on 4-manifolds
    • Chang, S.-Y. A.; Gursky, M. J.; Yang, P. C. An a priori estimate for a fully nonlinear equation on 4-manifolds. J. Anal. Math. 87 (2002), 151-186.
    • (2002) J. Anal. Math. , vol.87 , pp. 151-186
    • Chang, S.-Y.A.1    Gursky, M.J.2    Yang, P.C.3
  • 14
    • 0036587626 scopus 로고    scopus 로고
    • An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
    • Chang, S.-Y. A.; Gursky, M. J.; Yang, P. C. An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. of Math. 155 (2002), no. 3, 711-789.
    • (2002) Ann. of Math. , vol.155 , Issue.3 , pp. 711-789
    • Chang, S.-Y.A.1    Gursky, M.J.2    Yang, P.C.3
  • 16
    • 0031190439 scopus 로고    scopus 로고
    • The zeta functional determinants on manifolds with boundary. I. The formula
    • Chang, S.-Y. A.; Qing, J. The zeta functional determinants on manifolds with boundary. I. The formula. J. Funct. Anal. 147 (1997), no. 2, 327-362.
    • (1997) J. Funct. Anal. , vol.147 , Issue.2 , pp. 327-362
    • Chang, S.-Y.A.1    Qing, J.2
  • 17
    • 0031190766 scopus 로고    scopus 로고
    • The zeta functional determinants on manifolds with boundary. II. Extremal metrics and compactness of isospectral set
    • Chang, S.-Y. A.; Qing, J. The zeta functional determinants on manifolds with boundary. II. Extremal metrics and compactness of isospectral set. J. Funct. Anal. 147 (1997), no. 2, 363-399.
    • (1997) J. Funct. Anal. , vol.147 , Issue.2 , pp. 363-399
    • Chang, S.-Y.A.1    Qing, J.2
  • 20
    • 0000270633 scopus 로고
    • Extremal metrics of zeta function determinants on 4-manifolds
    • Chang, S.-Y. A.; Yang, P. C. Extremal metrics of zeta function determinants on 4-manifolds. Ann. of Math. (2) 142 (1995), no. 1, 171-212.
    • (1995) Ann. of Math. (2) , vol.142 , Issue.1 , pp. 171-212
    • Chang, S.-Y.A.1    Yang, P.C.2
  • 22
    • 84968494184 scopus 로고
    • A Trüdinger inequality on surfaces with conical singularities
    • Chen, W. X. A Trüdinger inequality on surfaces with conical singularities. Proc. Amer. Math. Soc. 108 (1990), no. 3, 821-832.
    • (1990) Proc. Amer. Math. Soc. , vol.108 , Issue.3 , pp. 821-832
    • Chen, W.X.1
  • 23
    • 0001378560 scopus 로고    scopus 로고
    • Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere
    • Ding, W.; Jost, J.; Li, J.; Wang, G. Multiplicity results for the two-vortex Chern-Simons Higgs model on the two-sphere. Comment. Math. Helv. 74 (1999), no. 1, 118-142.
    • (1999) Comment. Math. Helv. , vol.74 , Issue.1 , pp. 118-142
    • Ding, W.1    Jost, J.2    Li, J.3    Wang, G.4
  • 25
    • 84990553687 scopus 로고
    • Classical solutions of fully nonlinear, convex, second-order elliptic equations
    • Evans, L. C. Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math. 35 (1982), no. 3, 333-363.
    • (1982) Comm. Pure Appl. Math. , vol.35 , Issue.3 , pp. 333-363
    • Evans, L.C.1
  • 26
    • 0002406575 scopus 로고
    • Conformal invariants
    • Numero Hors Serie
    • Fefferman, C.; Graham, C. R. Conformal invariants. Astérisque 1985, Numero Hors Serie, 95-116.
    • (1985) Astérisque , pp. 95-116
    • Fefferman, C.1    Graham, C.R.2
  • 27
    • 51249167010 scopus 로고
    • Extremal functions for the Trudinger-Moser inequality in 2 dimensions
    • Flücher, M. Extremal functions for the Trudinger-Moser inequality in 2 dimensions. Comment. Math. Helv. 67 (1992), no. 3, 471-497.
    • (1992) Comment. Math. Helv. , vol.67 , Issue.3 , pp. 471-497
    • Flücher, M.1
  • 28
    • 51249162406 scopus 로고
    • Sharp borderline Sobolev inequalities on compact Riemannian manifolds
    • Fontana, L. Sharp borderline Sobolev inequalities on compact Riemannian manifolds. Comment. Math. Helv. 68 (1993), no. 3, 415-454.
    • (1993) Comment. Math. Helv. , vol.68 , Issue.3 , pp. 415-454
    • Fontana, L.1
  • 30
    • 0032359906 scopus 로고    scopus 로고
    • The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics
    • Gursky, M. J. The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics. Ann. of Math. (2) 148 (1998), no. 1, 315-337.
    • (1998) Ann. of Math. (2) , vol.148 , Issue.1 , pp. 315-337
    • Gursky, M.J.1
  • 31
    • 0033216642 scopus 로고    scopus 로고
    • The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE
    • Gursky, M. J. The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE. Comm. Math. Phys. 207 (1999), no. 1, 131-143.
    • (1999) Comm. Math. Phys. , vol.207 , Issue.1 , pp. 131-143
    • Gursky, M.J.1
  • 32
    • 84974003337 scopus 로고
    • 2
    • 2. Duke Math. J. 61 (1990), no. 3, 679-703.
    • (1990) Duke Math. J. , vol.61 , Issue.3 , pp. 679-703
    • Han, Z.-C.1
  • 33
    • 84968494937 scopus 로고
    • A best constant and the Gaussian curvature
    • Hong, C. W. A best constant and the Gaussian curvature. Proc. Amer. Math. Soc. 97 (1986), no. 4, 737-747.
    • (1986) Proc. Amer. Math. Soc. , vol.97 , Issue.4 , pp. 737-747
    • Hong, C.W.1
  • 34
    • 0000049367 scopus 로고
    • Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
    • Kazdan, J. L.; Warner, F. W. Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures. Ann. of Math. (2) 101 (1975), 317-331.
    • (1975) Ann. of Math. (2) , vol.101 , pp. 317-331
    • Kazdan, J.L.1    Warner, F.W.2
  • 35
    • 0000396066 scopus 로고
    • Boundedly inhomogeneous elliptic and parabolic equations
    • Krylov, N. V. Boundedly inhomogeneous elliptic and parabolic equations. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487-523; translation in Math. USSR Izv. 20 (1983), 459-492.
    • (1982) Izv. Akad. Nauk SSSR Ser. Mat. , vol.46 , Issue.3 , pp. 487-523
    • Krylov, N.V.1
  • 36
    • 84878313116 scopus 로고
    • translation
    • Krylov, N. V. Boundedly inhomogeneous elliptic and parabolic equations. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 3, 487-523; translation in Math. USSR Izv. 20 (1983), 459-492.
    • (1983) Math. USSR Izv. , vol.20 , pp. 459-492
  • 37
    • 0002383302 scopus 로고    scopus 로고
    • A sharp characterization of the smooth 4-sphere in curvature terms
    • Margerin, C. A sharp characterization of the smooth 4-sphere in curvature terms. Comm. Anal. Geom. 6 (1998), no. 1, 21-65.
    • (1998) Comm. Anal. Geom. , vol.6 , Issue.1 , pp. 21-65
    • Margerin, C.1
  • 38
    • 0001173833 scopus 로고
    • A sharp form of an inequality by N. Trudinger
    • Moser, J. A sharp form of an inequality by N. Trudinger. Indiana Univ. Math. J. 20 (1970/71), 1077-1092.
    • (1970) Indiana Univ. Math. J. , vol.20 , pp. 1077-1092
    • Moser, J.1
  • 40
    • 0001339558 scopus 로고
    • On the positivity of the effective action in a theory of random surfaces
    • Onofri, E. On the positivity of the effective action in a theory of random surfaces. Comm. Math. Phys. 86 (1982), no. 3, 321-326.
    • (1982) Comm. Math. Phys. , vol.86 , Issue.3 , pp. 321-326
    • Onofri, E.1
  • 41
    • 45449124033 scopus 로고
    • Compact isospectral sets of surfaces
    • Osgood, B.; Phillips, R.; Sarnak, P. Compact isospectral sets of surfaces. J. Funct. Anal. 80 (1988), no. 1, 212-234.
    • (1988) J. Funct. Anal. , vol.80 , Issue.1 , pp. 212-234
    • Osgood, B.1    Phillips, R.2    Sarnak, P.3
  • 42
    • 0000193161 scopus 로고
    • Extremals of determinants of Laplacians
    • Osgood, B.; Phillips, R.; Sarnak, P. Extremals of determinants of Laplacians. J. Funct. Anal. 80 (1988), no. 1, 148-211.
    • (1988) J. Funct. Anal. , vol.80 , Issue.1 , pp. 148-211
    • Osgood, B.1    Phillips, R.2    Sarnak, P.3
  • 45
    • 4243226043 scopus 로고
    • Quantum geometry of bosonic strings
    • Polyakov, A. M. Quantum geometry of bosonic strings. Phys. Lett. B 103 (1981), no. 3, 207-210.
    • (1981) Phys. Lett. B , vol.103 , Issue.3 , pp. 207-210
    • Polyakov, A.M.1
  • 46
    • 0000119424 scopus 로고
    • R-torsion and the Laplacian on Riemannian manifolds
    • Ray, D. B.; Singer, I. M. R-torsion and the Laplacian on Riemannian manifolds. Advances in Math. 7 (1971), 145-210.
    • (1971) Advances in Math. , vol.7 , pp. 145-210
    • Ray, D.B.1    Singer, I.M.2
  • 47
    • 0000858517 scopus 로고
    • The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group
    • Siu, Y. T. The existence of Kähler-Einstein metrics on manifolds with positive anticanonical line bundle and a suitable finite symmetry group. Ann. of Math. (2) 127 (1988), no. 3, 585-627.
    • (1988) Ann. of Math. (2) , vol.127 , Issue.3 , pp. 585-627
    • Siu, Y.T.1
  • 48
    • 2442535252 scopus 로고
    • Thesis, University of California, Los Angeles
    • 4. Thesis, University of California, Los Angeles, 1991.
    • (1991) 4
    • Soong, T.L.1
  • 50
    • 0030506073 scopus 로고    scopus 로고
    • Multiple condensate solutions for the Chern-Simons-Higgs theory
    • Tarantello, G. Multiple condensate solutions for the Chern-Simons-Higgs theory. J. Math. Phys. 37 (1996), no. 8, 3769-3796.
    • (1996) J. Math. Phys. , vol.37 , Issue.8 , pp. 3769-3796
    • Tarantello, G.1
  • 51
    • 0038967641 scopus 로고    scopus 로고
    • Kähler-Einstein metrics with positive scalar curvature
    • Tian, G. Kähler-Einstein metrics with positive scalar curvature. Invent. Math. 130 (1997), no. 1, 1-37.
    • (1997) Invent. Math. , vol.130 , Issue.1 , pp. 1-37
    • Tian, G.1
  • 52
    • 0000453612 scopus 로고
    • On imbeddings into Orlicz spaces and some applications
    • Trudinger, N. D. On imbeddings into Orlicz spaces and some applications. J. Math. Mech. 17 (1967), 473-483.
    • (1967) J. Math. Mech. , vol.17 , pp. 473-483
    • Trudinger, N.D.1
  • 53
    • 0034134398 scopus 로고    scopus 로고
    • Conformal geometry, contact geometry, and the calculus of variations
    • Viaclovsky, J. A. Conformal geometry, contact geometry, and the calculus of variations. Duke Math. J. 101 (2000), no. 2, 283-316.
    • (2000) Duke Math. J. , vol.101 , Issue.2 , pp. 283-316
    • Viaclovsky, J.A.1
  • 54
    • 23044518718 scopus 로고    scopus 로고
    • Conformally invariant Monge-Ampère equations: Global solutions
    • Viaclovsky, J. A. Conformally invariant Monge-Ampère equations: global solutions. Trans. Amer. Math. Soc. 352 (2000), no. 9, 4371-4379.
    • (2000) Trans. Amer. Math. Soc. , vol.352 , Issue.9 , pp. 4371-4379
    • Viaclovsky, J.A.1
  • 55
    • 0042995511 scopus 로고    scopus 로고
    • On a system of nonlinear elliptic equations arising in theoretical physics
    • Yang, Y. On a system of nonlinear elliptic equations arising in theoretical physics. J. Funct. Anal. 170 (2000), no. 1, 1-36.
    • (2000) J. Funct. Anal. , vol.170 , Issue.1 , pp. 1-36
    • Yang, Y.1
  • 56
    • 0002874135 scopus 로고
    • Global existence and convergence of Yamabe flow
    • Ye, R. Global existence and convergence of Yamabe flow. J. Differential Geom. 39 (1994), no. 1, 35-50.
    • (1994) J. Differential Geom. , vol.39 , Issue.1 , pp. 35-50
    • Ye, R.1


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