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Volumn 6, Issue SUPPL. 1, 2003, Pages 29-38

On the compactness of manifolds

Author keywords

Compactness; Curvature; Functional inequality; Riemannian manifolds

Indexed keywords


EID: 7244226599     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025703001249     Document Type: Review
Times cited : (7)

References (21)
  • 2
    • 0031138826 scopus 로고    scopus 로고
    • On Harnack estimates for positive solutions of the heat equation on a complete manifold
    • D. Bakry and Z. Qian, On Harnack estimates for positive solutions of the heat equation on a complete manifold, C. R. Acad. Paris I 324 (1997) 1037-1040.
    • (1997) C. R. Acad. Paris I , vol.324 , pp. 1037-1040
    • Bakry, D.1    Qian, Z.2
  • 3
    • 0039444272 scopus 로고    scopus 로고
    • Harnack inequalities on a manifold with positive or negative Ricci curvature
    • D. Bakry and Z. Qian, Harnack inequalities on a manifold with positive or negative Ricci curvature, Rev. Mat. Iberoamericana 15 (1999) 143-179.
    • (1999) Rev. Mat. Iberoamericana , vol.15 , pp. 143-179
    • Bakry, D.1    Qian, Z.2
  • 4
    • 7244248234 scopus 로고
    • Mémoire sue la théorie généales des surfaces
    • O. Bonnet, Mémoire sue la théorie généales des surfaces, J. lécole polytechnique 32 (1948) 1-48.
    • (1948) J. Lécole Polytechnique , vol.32 , pp. 1-48
    • Bonnet, O.1
  • 5
    • 22444452292 scopus 로고    scopus 로고
    • The heat kernel weighted Hodge Laplacian on noncompact manifolds
    • E. L. Buler, The heat kernel weighted Hodge Laplacian on noncompact manifolds, Trans. Amer. Math. Soc. 351 (1999) 683-714.
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 683-714
    • Buler, E.L.1
  • 7
    • 21744453864 scopus 로고    scopus 로고
    • Estimation of spectral gap for elliptic operators
    • M.-F. Chen and F.-Y. Wang, Estimation of spectral gap for elliptic operators, Trans. Amer. Math. Soc. 349 (1997) 1239-1267.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 1239-1267
    • Chen, M.-F.1    Wang, F.-Y.2
  • 8
    • 7244222902 scopus 로고    scopus 로고
    • Pure point spectrum and negative curvature for noncompact manifolds
    • H. Donnely and P. Li, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J. 46 (1997) 505-527.
    • (1997) Duke Math. J. , vol.46 , pp. 505-527
    • Donnely, H.1    Li, P.2
  • 9
    • 0042991111 scopus 로고
    • Curvature and Topology: Spectral positivity
    • Voronezh Series on New Developments in Global Analysis, ed. Yu Cliklikh
    • K. D. Elworthy, Xue-Mei Li, Steven Rosenberg, Curvature and Topology: spectral positivity, In Methods and Applications of Global Aanalysis, Voronezh Series on New Developments in Global Analysis, ed. Yu Cliklikh (1993) 45-60.
    • (1993) Methods and Applications of Global Aanalysis , pp. 45-60
    • Elworthy, K.D.1    Li, X.-M.2    Rosenberg, S.3
  • 10
    • 84966220264 scopus 로고
    • Compactness criteria for Riemannian manifolds
    • G. J. Galloway, Compactness criteria for Riemannian manifolds, Proc. Amer. Math. Soc. 84 (1982) 106-110.
    • (1982) Proc. Amer. Math. Soc. , vol.84 , pp. 106-110
    • Galloway, G.J.1
  • 11
    • 0035592025 scopus 로고    scopus 로고
    • Heat kernel estimates with application to compactness of manifolds
    • F.-Z. Gong and F.-Y. Wang, Heat kernel estimates with application to compactness of manifolds, Quart. J. Math. 52 (2001) 171-180.
    • (2001) Quart. J. Math. , vol.52 , pp. 171-180
    • Gong, F.-Z.1    Wang, F.-Y.2
  • 13
    • 0009337398 scopus 로고
    • Remarks on logarithmic Sobolev constants, exponential integrability and bounds on diameters
    • M. Ledoux, Remarks on logarithmic Sobolev constants, exponential integrability and bounds on diameters, J. Math. Kyoto Univ. 35 (1995) 211-220.
    • (1995) J. Math. Kyoto Univ. , vol.35 , pp. 211-220
    • Ledoux, M.1
  • 14
    • 0000458262 scopus 로고    scopus 로고
    • Concentration of measure and logarithmic Sobolev inequalities
    • M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, Lecture Notes in Math. No. 1709, 120-216, 1999.
    • (1999) Lecture Notes in Math. No. 1709 , pp. 120-216
    • Ledoux, M.1
  • 15
    • 0013555422 scopus 로고
    • On extension of Myers' theorem
    • X.-M. Li, On extension of Myers' theorem, Bull. Lond. Math. Soc. 27 (1995) 392-396.
    • (1995) Bull. Lond. Math. Soc. , vol.27 , pp. 392-396
    • Li, X.-M.1
  • 16
    • 84972530314 scopus 로고
    • Riemannian manifolds with positive mean curvature
    • S. B. Myers, Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941) 401-404.
    • (1941) Duke Math. J. , vol.8 , pp. 401-404
    • Myers, S.B.1
  • 17
    • 0032383993 scopus 로고    scopus 로고
    • A comparison theorem for an elliptic operator
    • Z. Qian, A comparison theorem for an elliptic operator, Potential Anal. 8 (1998) 137-142.
    • (1998) Potential Anal. , vol.8 , pp. 137-142
    • Qian, Z.1
  • 18
    • 0039605295 scopus 로고
    • Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below
    • L. Saloff-Coste, Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below, Coll. Math. 67 (1994) 109-121.
    • (1994) Coll. Math. , vol.67 , pp. 109-121
    • Saloff-Coste, L.1
  • 19
    • 0000593993 scopus 로고    scopus 로고
    • Functional inequalities for empty essential spectrum
    • F.-Y. Wang, Functional inequalities for empty essential spectrum, J. Funct. Anal. 170 (2000) 219-245.
    • (2000) J. Funct. Anal. , vol.170 , pp. 219-245
    • Wang, F.-Y.1
  • 20
    • 0000038655 scopus 로고    scopus 로고
    • Uniformly integrable operators and large deviations for Markov processes
    • L. Wu, Uniformly integrable operators and large deviations for Markov processes, J. Funct. Anal. 172 (2000) 301-376.
    • (2000) J. Funct. Anal. , vol.172 , pp. 301-376
    • Wu, L.1
  • 21
    • 0000567770 scopus 로고
    • Function theoretic properties of complete Riemannian manifolds and their applications in geometry
    • S.-T. Yau, Function theoretic properties of complete Riemannian manifolds and their applications in geometry, Indiana Univ. Math. J. 25 (1976) 659-670.
    • (1976) Indiana Univ. Math. J. , vol.25 , pp. 659-670
    • Yau, S.-T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.