메뉴 건너뛰기




Volumn 131, Issue 4, 2003, Pages 1283-1288

A remark on the maximum principle and stochastic completeness

Author keywords

Maximum principle; Stochastic completeness

Indexed keywords


EID: 0037385520     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-02-06672-8     Document Type: Conference Paper
Times cited : (123)

References (26)
  • 1
    • 0002524069 scopus 로고
    • Behaviour of diffusion semi-groups at infinity
    • [A] MR 50:8725
    • [A] R. Azencott, Behaviour of diffusion semi-groups at infinity, Bull. Soc. Math. France 102 (1974), 193-240. MR 50:8725
    • (1974) Bull. Soc. Math. France , vol.102 , pp. 193-240
    • Azencott, R.1
  • 2
    • 0012862739 scopus 로고    scopus 로고
    • Notes sur la démonstration de nadirashvili des conjectures de hadamard et Calabi-Yau
    • [CR] MR 2000i:53011
    • [CR] P. Collin and H. Rosenberg, Notes sur la démonstration de Nadirashvili des conjectures de Hadamard et Calabi-Yau, Bull. Sc. Math. 123 (1999), 563-575. MR 2000i:53011
    • (1999) Bull. Sc. Math. , vol.123 , pp. 563-575
    • Collin, P.1    Rosenberg, H.2
  • 3
    • 0000645210 scopus 로고
    • A generalized maximum principle and its applications in geometry
    • [CX] MR 93g:53054
    • [CX] Q. Chen and Y.L. Xin, A generalized maximum principle and its applications in geometry, Amer. J. Math. 114 (1992), 355-366. MR 93g:53054
    • (1992) Amer. J. Math. , vol.114 , pp. 355-366
    • Chen, Q.1    Xin, Y.L.2
  • 4
    • 84980189206 scopus 로고
    • Differential equations on Riemanninan manifolds and their geometric applications
    • [CY] MR 52:6608
    • [CY] S.Y. Cheng and S.T. Yau, Differential equations on Riemanninan manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354. MR 52:6608
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 333-354
    • Cheng, S.Y.1    Yau, S.T.2
  • 6
    • 0003335976 scopus 로고
    • Selected topics in harmonic maps
    • [EL] AMS, Providence. MR 85g:58030
    • [EL] J. Eells and L. Lemaire, Selected Topics in Harmonic Maps, CBMS n. 50, AMS, Providence, 1983. MR 85g:58030
    • (1983) CBMS , vol.50
    • Eells, J.1    Lemaire, L.2
  • 7
    • 0002892716 scopus 로고
    • Some rigidity theorems for minimal submanifolds of the sphere
    • [FC] MR 82b:53078
    • [FC] D. Fischer-Colbrie, Some rigidity theorems for minimal submanifolds of the sphere, Acta Math. 145 (1980), 29-46. MR 82b:53078
    • (1980) Acta Math. , vol.145 , pp. 29-46
    • Fischer-Colbrie, D.1
  • 8
    • 0002530893 scopus 로고
    • The conservation property of the heat equation on Riemannian manifolds
    • [G] MR 21:892
    • [G] M.P. Gaffney, The conservation property of the heat equation on Riemannian manifolds, Comm. Pure Appl. Math. 12 (1959), 1-11. MR 21:892
    • (1959) Comm. Pure Appl. Math. , vol.12 , pp. 1-11
    • Gaffney, M.P.1
  • 9
    • 0000070043 scopus 로고
    • On stochastically complete manifolds
    • [Gr1] MR 88a:58209
    • [Gr1] A. Grigor'yan, On stochastically complete manifolds, Engl. Transl. Soviet Math. Dokl. 34 (1987), 310-313. MR 88a:58209
    • (1987) Engl. Transl. Soviet Math. Dokl. , vol.34 , pp. 310-313
    • Grigor'yan, A.1
  • 10
    • 0011009170 scopus 로고
    • Bounded solutions of the Schrödinger equation on non-compact Riemannian manifolds
    • [Gr2] MR 90m:35050
    • [Gr2] A. Grigor'yan, Bounded solutions of the Schrödinger equation on non-compact Riemannian manifolds, Engl. Transl. J. of Soviet Math. 51 (1990), 2340-2349. MR 90m:35050
    • (1990) Engl. Transl. J. of Soviet Math. , vol.51 , pp. 2340-2349
    • Grigor'yan, A.1
  • 11
    • 0039657135 scopus 로고    scopus 로고
    • Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
    • [Gr3] MR 99k:58195
    • [Gr3] A. Grigor'yan, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. 36 (1999), 135-249. MR 99k:58195
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 135-249
    • Grigor'yan, A.1
  • 12
    • 0001474422 scopus 로고
    • Function theory on manifolds which possess a pole
    • [GW] Springer Verlag, Berlin, MR 81a:53002
    • [GW] R. Greene and H.H. Wu, Function Theory on Manifolds Which Possess a Pole, Lecture Notes in Math. n. 699, Springer Verlag, Berlin, 1979 MR 81a:53002
    • (1979) Lecture Notes in Math. , Issue.699
    • Greene, R.1    Wu, H.H.2
  • 13
    • 0000936684 scopus 로고
    • The strong halfspace theorem for minimal surfaces
    • [HM] MR 92e:53010
    • [HM] D. Hoffman and W. Meeks, The strong halfspace theorem for minimal surfaces, Invent. Math. 101 (1990), 373-377. MR 92e:53010
    • (1990) Invent. Math. , vol.101 , pp. 373-377
    • Hoffman, D.1    Meeks, W.2
  • 14
    • 34250112419 scopus 로고
    • Differential inequalities on complete Riemannian manifolds and applications
    • [K]. MR 87g:58119
    • [K] L. Karp, Differential inequalities on complete Riemannian manifolds and applications, Math. Ann. 272 (1985), 449-459. MR 87g:58119
    • (1985) Math. Ann. , vol.272 , pp. 449-459
    • Karp, L.1
  • 15
    • 0012893496 scopus 로고
    • Estimates for solutions of Poisson equations and their applications to submanifolds
    • [Ks] MR 86d:58118
    • [Ks] A. Kasue, Estimates for solutions of Poisson equations and their applications to submanifolds, Springer Lecture Notes in Mathematics 1090 (1984), 1-14. MR 86d:58118
    • (1984) Springer Lecture Notes in Mathematics , vol.1090 , pp. 1-14
    • Kasue, A.1
  • 16
    • 84972528441 scopus 로고
    • 1 solutions for the Laplace equation and the heat equation on Riemannian manifolds
    • [L] MR 86h:58133
    • 1 solutions for the Laplace equation and the heat equation on Riemannian manifolds, J, Diff. Geom. 20 (1984), 447-457. MR 86h:58133
    • (1984) J. Diff. Geom. , vol.20 , pp. 447-457
    • Li, P.1
  • 17
    • 0002433346 scopus 로고
    • Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions
    • [MY]. MR 85j:53068
    • [MY] N. Mok and S.T. Yau, Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions, Proc. Symp. Pure Math. 39 (1983), 41-59. MR 85j:53068
    • (1983) Proc. Symp. Pure Math. , vol.39 , pp. 41-59
    • Mok, N.1    Yau, S.T.2
  • 18
    • 0030509351 scopus 로고    scopus 로고
    • Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces
    • [N] MR 98d:53014
    • [N] N.S. Nadirashvili, Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces, Invent. Math. 126 (1996), 457-465. MR 98d:53014
    • (1996) Invent. Math. , vol.126 , pp. 457-465
    • Nadirashvili, N.S.1
  • 19
    • 84972539418 scopus 로고
    • Isometric immersions of Riemannian manifolds
    • [O] MR 35:6101
    • [O] H. Omori, Isometric immersions of Riemannian manifolds, J. Math. Soc. Japan 19 (1967), 205-214. MR 35:6101
    • (1967) J. Math. Soc. Japan , vol.19 , pp. 205-214
    • Omori, H.1
  • 20
    • 51249186499 scopus 로고
    • The Ahlfors-Schwarz lemma in several complex variables
    • [R] MR 82i:32049
    • [R] H.L. Royden, The Ahlfors-Schwarz lemma in several complex variables, Comm. Math. Helv. 55 (1980), 547-558. MR 82i:32049
    • (1980) Comm. Math. Helv. , vol.55 , pp. 547-558
    • Royden, H.L.1
  • 21
    • 0000813466 scopus 로고
    • On the Omori-Yau maximum principle and its applications to differential equations and geometry
    • [RRS] MR 96k:53062
    • [RRS] A. Ratto, M. Rigoli and A.G. Setti, On the Omori-Yau maximum principle and its applications to differential equations and geometry, J. Funct. Anal. 134 (1995), 486-510. MR 96k:53062
    • (1995) J. Funct. Anal. , vol.134 , pp. 486-510
    • Ratto, A.1    Rigoli, M.2    Setti, A.G.3
  • 22
    • 0002728521 scopus 로고
    • Scalar curvature and conformal deformation of hyperbolic space
    • [RRV]. MR 95a:53062
    • [RRV] A. Ratto, M. Rigoli and L. Veron, Scalar curvature and conformal deformation of hyperbolic space, J. Funct. Anal. 121 (1994), 15-77. MR 95a:53062
    • (1994) J. Funct. Anal. , vol.121 , pp. 15-77
    • Ratto, A.1    Rigoli, M.2    Veron, L.3
  • 23
    • 0012790259 scopus 로고    scopus 로고
    • A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds
    • [T] MR 99i:53042
    • [T] K. Takegoshi, A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds, Nagoya Math. J. 151 (1998), 25-36. MR 99i:53042
    • (1998) Nagoya Math. J. , vol.151 , pp. 25-36
    • Takegoshi, K.1
  • 24
    • 0000411710 scopus 로고
    • On the heat kernel of a complete Riemannian manifold
    • [Y1] MR 81b:58041
    • [Y1] S.T. Yau, On the heat kernel of a complete Riemannian manifold, J. Math. Pures Appl. 57 (1978), 191-201. MR 81b:58041
    • (1978) J. Math. Pures Appl. , vol.57 , pp. 191-201
    • Yau, S.T.1
  • 25
    • 84980178548 scopus 로고
    • Harmonic functions on complete Riemannian manifolds
    • [Y2] MR 55:4042
    • [Y2] S.T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228. MR 55:4042
    • (1975) Comm. Pure Appl. Math. , vol.28 , pp. 201-228
    • Yau, S.T.1
  • 26
    • 0000541075 scopus 로고
    • A general Schwarz lemma for Kähler manifolds
    • [Y3] MR 58:6370
    • [Y3] S.T. Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), 197-203. MR 58:6370
    • (1978) Amer. J. Math. , vol.100 , pp. 197-203
    • Yau, S.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.