메뉴 건너뛰기




Volumn 61, Issue 11, 2008, Pages 1540-1602

Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications

Author keywords

[No Author keywords available]

Indexed keywords


EID: 53649093968     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20232     Document Type: Article
Times cited : (12)

References (27)
  • 1
    • 84968470198 scopus 로고
    • An extension of Schwarz's lemma
    • Ahlfors, L. V. An extension of Schwarz's lemma. Trans. Amer. Math. Soc. 43 (1938), no. 3, 359-364.
    • (1938) Trans. Amer. Math. Soc , vol.43 , Issue.3 , pp. 359-364
    • Ahlfors, L.V.1
  • 2
    • 0001104071 scopus 로고
    • A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order
    • Aronszajn, N. A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. (9) 36 (1957), 235-249.
    • (1957) J. Math. Pures Appl. (9) , vol.36 , pp. 235-249
    • Aronszajn, N.1
  • 3
    • 34250084341 scopus 로고
    • Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations
    • Bourgain, J. Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3 (1993), no. 2, 107-156.
    • (1993) Geom. Funct. Anal , vol.3 , Issue.2 , pp. 107-156
    • Bourgain, J.1
  • 4
    • 12144282712 scopus 로고    scopus 로고
    • Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces
    • Burq, N.; Gérard, P.; Tzvetkov, N. Bilinear eigenfunction estimates and the nonlinear Schrödinger equation on surfaces. Invent. Math. 159 (2005), no. 1, 187-223.
    • (2005) Invent. Math , vol.159 , Issue.1 , pp. 187-223
    • Burq, N.1    Gérard, P.2    Tzvetkov, N.3
  • 5
    • 84980189206 scopus 로고
    • Differential equations on Riemannian manifolds and their geometric applications
    • Cheng, S. Y.; Yau, S. T. Differential equations on Riemannian manifolds and their geometric applications. Comm. Pure Appl. Math. 28 (1975), no. 3, 333-354.
    • (1975) Comm. Pure Appl. Math , vol.28 , Issue.3 , pp. 333-354
    • Cheng, S.Y.1    Yau, S.T.2
  • 6
    • 5744252574 scopus 로고    scopus 로고
    • Singular limit laminations, Morse index, and positive scalar curvature
    • Colding, T. H.; De Lellis, C. Singular limit laminations, Morse index, and positive scalar curvature. Topology 44 (2005), no. 1, 25-45.
    • (2005) Topology , vol.44 , Issue.1 , pp. 25-45
    • Colding, T.H.1    De Lellis, C.2
  • 7
    • 33750889866 scopus 로고    scopus 로고
    • Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics
    • Colding, T. H.; Hingston, N. Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics. Comment. Math. Helv. 81 (2006), no. 3, 495-522.
    • (2006) Comment. Math. Helv , vol.81 , Issue.3 , pp. 495-522
    • Colding, T.H.1    Hingston, N.2
  • 8
    • 0031321696 scopus 로고    scopus 로고
    • Harmonic functions on manifolds
    • Colding, T. H.; Minicozzi, W. P., II. Harmonic functions on manifolds. Ann. of Math. (2) 146 (1997), no. 3, 725-747.
    • (1997) Ann. of Math. (2) , vol.146 , Issue.3 , pp. 725-747
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 9
    • 0002733807 scopus 로고    scopus 로고
    • Harmonic functions with polynomial growth
    • Colding, T. H.; Minicozzi, W. P., II. Harmonic functions with polynomial growth. J. Differential Geom. 46(1997), no. 1, 1-77.
    • (1997) J. Differential Geom , vol.46 , Issue.1 , pp. 1-77
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 10
    • 0003284040 scopus 로고    scopus 로고
    • Minimal surfaces
    • New York University, Courant Institute of Mathematical Sciences, New York
    • Colding, T. H.; Minicozzi, W. P., II. Minimal surfaces. Courant Lecture Notes in Mathematics, 4. New York University, Courant Institute of Mathematical Sciences, New York, 1999.
    • (1999) Courant Lecture Notes in Mathematics , vol.4
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 11
    • 0742271508 scopus 로고    scopus 로고
    • Embedded minimal disks: Proper versus nonproper - global versus local
    • electronic
    • Colding, T. H.; Minicozzi, W. P., II. Embedded minimal disks: proper versus nonproper - global versus local. Trans. Amer. Math. Soc. 356 (2004), no. 1, 283-289 (electronic).
    • (2004) Trans. Amer. Math. Soc , vol.356 , Issue.1 , pp. 283-289
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 12
    • 15744369838 scopus 로고    scopus 로고
    • The space of embedded minimal surfaces of fixed genus in a 3-manifold. I. Estimates off the axis for disks
    • Colding, T. H.; Minicozzi, W. P., II. The space of embedded minimal surfaces of fixed genus in a 3-manifold. I. Estimates off the axis for disks. Ann. of Math. (2) 160 (2004), no. 1, 27-68.
    • (2004) Ann. of Math. (2) , vol.160 , Issue.1 , pp. 27-68
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 13
    • 15744370308 scopus 로고    scopus 로고
    • The space of embedded minimal surfaces of fixed genus in a 3-manifold. II. Multi-valued graphs in disks
    • Colding, T. H.; Minicozzi, W. P., II. The space of embedded minimal surfaces of fixed genus in a 3-manifold. II. Multi-valued graphs in disks. Ann. of Math. (2) 160 (2004), no. 1, 69-92.
    • (2004) Ann. of Math. (2) , vol.160 , Issue.1 , pp. 69-92
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 14
    • 15944399783 scopus 로고    scopus 로고
    • The space of embedded minimal surfaces of fixed genus in a 3-manifold. III. Planar domains
    • Colding, T. H.; Minicozzi, W. P., II. The space of embedded minimal surfaces of fixed genus in a 3-manifold. III. Planar domains. Ann. of Math. (2) 160 (2004), no. 2, 523-572.
    • (2004) Ann. of Math. (2) , vol.160 , Issue.2 , pp. 523-572
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 15
    • 15944384972 scopus 로고    scopus 로고
    • The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV. Locally simply connected
    • Colding, T. H.; Minicozzi, W. P., II. The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV. Locally simply connected. Ann. of Math. (2) 160 (2004), no. 2, 573-615.
    • (2004) Ann. of Math. (2) , vol.160 , Issue.2 , pp. 573-615
    • Colding, T.H.1    Minicozzi II, W.P.2
  • 16
    • 53649105339 scopus 로고    scopus 로고
    • Colding, T. H.; Minicozzi, W. P., II. The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus. arXiv:math/0509647, 2005.
    • Colding, T. H.; Minicozzi, W. P., II. The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus. arXiv:math/0509647, 2005.
  • 17
    • 51249186551 scopus 로고
    • Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques.
    • Colin de Verdière, Y. Sur le spectre des opérateurs elliptiques à bicaractéristiques toutes périodiques. Comment. Math. Helv. 54 (1979), no. 3, 508-522.
    • (1979) Comment. Math. Helv , vol.54 , Issue.3 , pp. 508-522
    • Colin de Verdière, Y.1
  • 18
    • 84990604274 scopus 로고
    • Unique continuation for elliptic operators: A geometric-variational approach
    • Garofalo, N.; Lin, F.-H. Unique continuation for elliptic operators: a geometric-variational approach. Comm. Pure Appl. Math. 40 (1987), no. 3, 347-366.
    • (1987) Comm. Pure Appl. Math , vol.40 , Issue.3 , pp. 347-366
    • Garofalo, N.1    Lin, F.-H.2
  • 19
    • 53649085029 scopus 로고    scopus 로고
    • Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order. 2nd ed. Grundlehren der mathematischen Wissenschaften, 224. Springer, Berlin, 1983.
    • Gilbarg, D.; Trudinger, N. S. Elliptic partial differential equations of second order. 2nd ed. Grundlehren der mathematischen Wissenschaften, 224. Springer, Berlin, 1983.
  • 20
    • 84972548521 scopus 로고
    • Lectures on spectral theory of elliptic operators
    • Guillemin, V. Lectures on spectral theory of elliptic operators. Duke Math. J. 44 (1977), no. 3, 485-517.
    • (1977) Duke Math. J , vol.44 , Issue.3 , pp. 485-517
    • Guillemin, V.1
  • 21
    • 0346487086 scopus 로고    scopus 로고
    • Exponential growth solutions of elliptic equations
    • Hang, F.; Lin, F. Exponential growth solutions of elliptic equations. Acta Math. Sin. (Engl. Ser.) 15 (1999), no. 4, 525-534.
    • (1999) Acta Math. Sin. (Engl. Ser.) , vol.15 , Issue.4 , pp. 525-534
    • Hang, F.1    Lin, F.2
  • 23
    • 0001226256 scopus 로고
    • Unique continuation and absence of positive eigenvalues for Schrödinger operators
    • Jerison, D.; Kenig, C. E. Unique continuation and absence of positive eigenvalues for Schrödinger operators. Ann. of Math. (2) 121 (1985), no. 3, 463-494.
    • (1985) Ann. of Math. (2) , vol.121 , Issue.3 , pp. 463-494
    • Jerison, D.1    Kenig, C.E.2
  • 24
    • 1042308156 scopus 로고    scopus 로고
    • A remark on unique continuation
    • Pan, Y.; Wolff, T. A remark on unique continuation. J. Geom. Anal. 8 (1998), no. 4, 599-604.
    • (1998) J. Geom. Anal , vol.8 , Issue.4 , pp. 599-604
    • Pan, Y.1    Wolff, T.2
  • 25
    • 53649092433 scopus 로고    scopus 로고
    • Reed, M.; Simon, B. Methods of modern mathematical physics. IV. Analysis of operators. Academic Press, New York-London, 1978.
    • Reed, M.; Simon, B. Methods of modern mathematical physics. IV. Analysis of operators. Academic Press, New York-London, 1978.
  • 26
    • 84972497579 scopus 로고
    • New applications of mapping degrees to minimal surface theory
    • White, B. New applications of mapping degrees to minimal surface theory. J. Differential Geom. 29 (1989), no. 1, 143-162.
    • (1989) J. Differential Geom , vol.29 , Issue.1 , pp. 143-162
    • White, B.1
  • 27
    • 0039351671 scopus 로고
    • The space of minimal submanifolds for varying Riemannian metrics
    • White, B. The space of minimal submanifolds for varying Riemannian metrics. Indiana Univ. Math. J. 40 (1991), no. 1, 161-200.
    • (1991) Indiana Univ. Math. J , vol.40 , Issue.1 , pp. 161-200
    • White, B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.