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Volumn 97, Issue 2, 1999, Pages 319-346

Volume growth, green’s functions, and parabolicity of ends

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EID: 0039530432     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-09714-4     Document Type: Article
Times cited : (77)

References (49)
  • 1
    • 0000046378 scopus 로고
    • Lower curvature bounds, Toponogov's theorem, and bounded topology
    • U. Abresch, Lower curvature bounds, Toponogov's theorem, and bounded topology, Ann. Sci. École Norm. Sup. (4) 18 (1985), 651-670.
    • (1985) Ann. Sci. École Norm. Sup. , vol.4 , Issue.18 , pp. 651-670
    • Abresch, U.1
  • 2
    • 84968508874 scopus 로고
    • On complete manifolds with nonnegative Ricci curvature
    • U. Abresch and D. Gromoll, On complete manifolds with nonnegative Ricci curvature, J. Amer. Math. Soc. 3 (1990), 355-374.
    • (1990) J. Amer. Math. Soc , vol.3 , pp. 355-374
    • Abresch, U.1    Gromoll, D.2
  • 3
    • 0005212059 scopus 로고
    • Sur le type d'une surface de Riemann
    • L.V. Ahlfors, Sur le type d'une surface de Riemann, C. R. Acad. Sci. Paris Sér. A 201 (1935), 30-32.
    • (1935) C. R. Acad. Sci. Paris Sér. A , vol.201 , pp. 30-32
    • Ahlfors, L.V.1
  • 4
    • 0001274614 scopus 로고
    • Zur Theorie der Überlagerungsfíachen
    • L.V. Ahlfors, Zur Theorie der Überlagerungsfíachen, Acta Math. 65 (1935), 157-194.
    • (1935) Acta Math , vol.65 , pp. 157-194
    • Ahlfors, L.V.1
  • 5
    • 0013480391 scopus 로고
    • Geometry of Manifolds
    • Academic Press, New York
    • R. Bishop and R. Crittenden, Geometry of Manifolds, Pure Appl. Math. 15, Academic Press, New York, 1964.
    • (1964) Pure Appl. Math , vol.15
    • Bishop, R.1    Crittenden, R.2
  • 6
    • 0000720752 scopus 로고
    • A note on the isoperimetric constant
    • P. Buser, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. (4) 15 (1982), 213-230.
    • (1982) Ann. Sci. École Norm. Sup. , vol.4 , Issue.15 , pp. 213-230
    • Buser, P.1
  • 7
    • 84967780461 scopus 로고
    • Ends of Riemannian manifolds with nonnegative Ricci curvature outside a compact set
    • M. Cai, Ends of Riemannian manifolds with nonnegative Ricci curvature outside a compact set, Bull. Amer. Math. Soc. (N.S.) 24 (1991), 371-377.
    • (1991) Bull. Amer. Math. Soc. (N.S.) , vol.24 , pp. 371-377
    • Cai, M.1
  • 8
    • 84972500359 scopus 로고
    • The splitting theorem for manifolds of nonnegative Ricci curvature
    • J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geom. 6 (1971), 119-128.
    • (1971) J. Differential Geom , vol.6 , pp. 119-128
    • Cheeger, J.1    Gromoll, D.2
  • 9
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53.
    • (1982) J. Differential Geom , vol.17 , pp. 15-53
    • Cheeger, J.1    Gromov, M.2    Taylor, M.3
  • 10
    • 84980189206 scopus 로고
    • Differential equations on Riemannian manifolds and their geometric applications
    • S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), 333-354.
    • (1975) Comm. Pure Appl. Math , vol.28 , pp. 333-354
    • Cheng, S.Y.1    Yau, S.T.2
  • 11
    • 0042633317 scopus 로고
    • Variétés riemanniennes isométriques à l'infini
    • T. Coulhon and L. Saloff-Coste, Variétés riemanniennes isométriques à l'infini, Rev. Mat. Iberoamericana 11 (1995), 687-726.
    • (1995) Rev. Mat. Iberoamericana , vol.11 , pp. 687-726
    • Coulhon, T.1    Saloff-Coste, L.2
  • 12
    • 85037891354 scopus 로고    scopus 로고
    • Harnack inequality and hyperbolicity for the p-Laplacian with applications to quasiregular mappings
    • T. Coulhon and L. Saloff-Coste, Harnack inequality and hyperbolicity for the p-Laplacian with applications to quasiregular mappings, preprint.
    • Preprint
    • Coulhon, T.1    Saloff-Coste, L.2
  • 13
    • 0009897766 scopus 로고
    • On the existence of a Green function on a manifold (In Russian)
    • A. Grigor'yan, On the existence of a Green function on a manifold (in Russian), Uspekhi Mat. Nauk 38 (1983), 161-162;
    • (1983) Uspekhi Mat. Nauk , vol.38 , pp. 161-162
    • Grigor'yan, A.1
  • 15
    • 0000123369 scopus 로고
    • On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds (In Russian)
    • A. Grigor'yan, On the existence of positive fundamental solutions of the Laplace equation on Riemannian manifolds (in Russian), Mat. Sb. (N.S.) 128 (1985), 354-363;
    • (1985) Mat. Sb. (N.S.) , vol.128 , pp. 354-363
    • Grigor'yan, A.1
  • 17
    • 84956103754 scopus 로고
    • The heat equation on noncompact Riemannian manifolds
    • A. Grigor'yan, The heat equation on noncompact Riemannian manifolds, Math. USSR-Sb. 72 (1992), 47-77.
    • (1992) Math. Ussr-Sb , vol.72 , pp. 47-77
    • Grigor'yan, A.1
  • 20
    • 0010756253 scopus 로고
    • Nonlinear potential theory and quasiregular mappings on Riemannian manifolds
    • I. Holopainen, Nonlinear potential theory and quasiregular mappings on Riemannian manifolds, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 74 (1990), 1-45.
    • (1990) Ann. Acad. Sci. Fenn. Ser. a I Math. Dissertationes , vol.74 , pp. 1-45
    • Holopainen, I.1
  • 21
    • 84962991764 scopus 로고
    • Positive solutions of quasilinear elliptic equations on Riemannian manifolds
    • I. Holopainen, Positive solutions of quasilinear elliptic equations on Riemannian manifolds, Proc. London Math. Soc. (3) 65 (1992), 651-672.
    • (1992) Proc. London Math. Soc. , vol.3 , Issue.65 , pp. 651-672
    • Holopainen, I.1
  • 22
    • 51249165301 scopus 로고
    • Solutions of elliptic equations on manifolds with roughly Euclidean ends
    • I. Holopainen, Solutions of elliptic equations on manifolds with roughly Euclidean ends, Math. Z. 217 (1994), 459-477.
    • (1994) Math. Z , vol.217 , pp. 459-477
    • Holopainen, I.1
  • 23
    • 0002074324 scopus 로고    scopus 로고
    • Ricci curvature, Harnack functions, and Picard-type theorems for quasiregular mappings
    • C. Cazacu, O. Lehto, and T. Rassias, World Scientific, Singapore
    • I. Holopainen and S. Rickman, “Ricci curvature, Harnack functions, and Picard-type theorems for quasiregular mappings” in Analysis and Topology, ed. C. Cazacu, O. Lehto, and T. Rassias, World Scientific, Singapore, 1998, 315-326.
    • (1998) Analysis and Topology , pp. 315-326
    • Holopainen, I.1    Rickman, S.2
  • 24
    • 84972555264 scopus 로고
    • The Poincaré inequality for vector fields satisfying Hormander's condition
    • D. Jerison, The Poincaré inequality for vector fields satisfying Hormander's condition, Duke Math. J. 53 (1986), 503-523.
    • (1986) Duke Math. J , vol.53 , pp. 503-523
    • Jerison, D.1
  • 25
    • 84972557750 scopus 로고
    • Rough isometries and combinatorial approximations of geometries of noncompact Riemannian manifolds
    • M. Kanai, Rough isometries and combinatorial approximations of geometries of noncompact Riemannian manifolds, J. Math. Soc. Japan 37 (1985), 391-413.
    • (1985) J. Math. Soc. Japan , vol.37 , pp. 391-413
    • Kanai, M.1
  • 26
    • 0001446871 scopus 로고
    • A compactification of a manifold with asymptotically nonnegative curvature
    • A. Kasue, A compactification of a manifold with asymptotically nonnegative curvature, Ann. Sci. École Norm. Sup. (4) 21 (1988), 593-622.
    • (1988) Ann. Sci. École Norm. Sup. , vol.4 , Issue.21 , pp. 593-622
    • Kasue, A.1
  • 27
    • 0040149075 scopus 로고
    • Harmonic functions with growth conditions on a manifold of asymptotically nonnegative curvature, I
    • Springer-Verlag, Berlin
    • A. Kasue, “Harmonic functions with growth conditions on a manifold of asymptotically nonnegative curvature, I” in Geometry and Analysis on Manifolds, Lecture Notes in Math. 1339, Springer-Verlag, Berlin, 1988, 158-181.
    • (1988) Geometry and Analysis on Manifolds, Lecture Notes in Math , vol.1339 , pp. 158-181
    • Kasue, A.1
  • 28
    • 0040973054 scopus 로고
    • Riemannian manifolds of a-parabolic type (In Russian)
    • V. M. Kesel'man, Riemannian manifolds of a-parabolic type (in Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 4 (1985), 81-83, 88.
    • (1985) Izv. Vyssh. Uchebn. Zaved. Mat. 4 , vol.88 , pp. 81-83
    • Kesel'man, V.M.1
  • 29
    • 0005230872 scopus 로고    scopus 로고
    • On the conformal type of a Riemannian manifold
    • Russian
    • V. M. Kesel'man and V. A. Zorich, On the conformal type of a Riemannian manifold (in Russian), Funktsional. Anal. i Prilozhen. 30 (1996), 40-55, 96;
    • (1996) Funktsional. Anal. I Prilozhen , vol.30 , Issue.96 , pp. 40-55
    • Kesel'man, V.M.1    Zorich, V.A.2
  • 31
    • 0000111884 scopus 로고
    • The Wiener test and potential estimates for quasilinear elliptic equations
    • T. Kilpelainen and J. Maly, The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137-161.
    • (1994) Acta Math , vol.172 , pp. 137-161
    • Kilpelainen, T.1    Maly, J.2
  • 32
    • 85037873662 scopus 로고    scopus 로고
    • Curvature and function theory on Riemannian manifolds
    • P. Li, Curvature and function theory on Riemannian manifolds, preprint.
    • Preprint
    • Li, P.1
  • 33
    • 0000444319 scopus 로고
    • Positive harmonic functions on complete manifolds with nonnegative curvature outside a compact set
    • P. Li and L. F. Tam, Positive harmonic functions on complete manifolds with nonnegative curvature outside a compact set, Ann. of Math. (2) 125 (1987), 171-207.
    • (1987) Ann. of Math. , vol.125 , Issue.2 , pp. 171-207
    • Li, P.1    Tam, L.F.2
  • 34
    • 84972545905 scopus 로고
    • Harmonic functions and the structure of complete manifolds
    • P. Li and L. F. Tam, Harmonic functions and the structure of complete manifolds, J. Differential Geom. 35 (1992), 359-383.
    • (1992) J. Differential Geom , vol.35 , pp. 359-383
    • Li, P.1    Tam, L.F.2
  • 35
    • 84972525278 scopus 로고
    • Green's functions, harmonic functions, and volume comparison
    • P. Li and L. F. Tam, Green's functions, harmonic functions, and volume comparison, J. Differential Geom. 41 (1995), 277-318.
    • (1995) J. Differential Geom , vol.41 , pp. 277-318
    • Li, P.1    Tam, L.F.2
  • 36
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrodinger operator
    • P. Li and S. T. Yau, On the parabolic kernel of the Schrodinger operator, Acta Math. 156 (1986), 153-201.
    • (1986) Acta Math , vol.156 , pp. 153-201
    • Li, P.1    Yau, S.T.2
  • 37
    • 0001023172 scopus 로고
    • Two theorems of N. Wiener for solutions of quasilinear elliptic equations
    • P. Lindqvist and O. Martio, Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), 153-171.
    • (1985) Acta Math , vol.155 , pp. 153-171
    • Lindqvist, P.1    Martio, O.2
  • 38
    • 0002346286 scopus 로고
    • Ball covering property and nonnegative Ricci curvature outside a compact set
    • Differential Geometry: Riemannian Geometry, Amer. Math. Soc., Providence
    • Z. Liu, “Ball covering property and nonnegative Ricci curvature outside a compact set” in Differential Geometry: Riemannian Geometry, Proc. Sympos. Pure Math. 54, Amer. Math. Soc., Providence, 1993, 459-464.
    • (1993) Proc. Sympos. Pure Math , vol.54 , pp. 459-464
    • Liu, Z.1
  • 39
    • 0001235277 scopus 로고
    • On the continuity at a boundary point of solutions of quasilinear elliptic equations
    • V. G. Maz'ya, On the continuity at a boundary point of solutions of quasilinear elliptic equations, Vestnik Leningrad. Univ. Mat. 3 (1976), 225-242.
    • (1976) Vestnik Leningrad. Univ. Mat , vol.3 , pp. 225-242
    • Maz'ya, V.G.1
  • 41
    • 0039054422 scopus 로고    scopus 로고
    • A note on p-subharmonic functions on complete manifolds
    • M. Rigoli, M. Salvatori, and M. Vignati, A note on p-subharmonic functions on complete manifolds, Manuscripta Math. 92 (1997), 339-359.
    • (1997) Manuscripta Math , vol.92 , pp. 339-359
    • Rigoli, M.1    Salvatori, M.2    Vignati, M.3
  • 42
    • 84963021360 scopus 로고
    • A note on Poincaré, Sobolev, and Harnack inequalities
    • L. Saloff-Coste, A note on Poincaré, Sobolev, and Harnack inequalities, Internat. Math. Res. Notices 1992, 27-38.
    • (1992) Internat. Math. Res. Notices , pp. 27-38
    • Saloff-Coste, L.1
  • 43
    • 84972525827 scopus 로고
    • Uniformly elliptic operators on Riemannian manifolds
    • L. Saloff-Coste, Uniformly elliptic operators on Riemannian manifolds, J. Differential Geom. 36 (1992), 417-450.
    • (1992) J. Differential Geom , vol.36 , pp. 417-450
    • Saloff-Coste, L.1
  • 44
    • 0000798567 scopus 로고
    • Local behavior of solutions of quasi-linear equations
    • J. Serrin, Local behavior of solutions of quasi-linear equations, Acta Math. 111 (1964), 247-302.
    • (1964) Acta Math , vol.111 , pp. 247-302
    • Serrin, J.1
  • 45
    • 0001738334 scopus 로고
    • The Poisson kernel on positively curved manifolds
    • N. Varopoulos, The Poisson kernel on positively curved manifolds, J. Funct. Anal. 44 (1981), 359-380.
    • (1981) J. Funct. Anal , vol.44 , pp. 359-380
    • Varopoulos, N.1
  • 46
    • 0040597940 scopus 로고
    • Green's functions on positively curved manifolds
    • N. Varopoulos, Green's functions on positively curved manifolds, J. Funct. Anal. 45 (1982), 109-118.
    • (1982) J. Funct. Anal , vol.45 , pp. 109-118
    • Varopoulos, N.1
  • 47
    • 0001598968 scopus 로고
    • Potential theory and diffusion on Riemannian manifolds
    • Wadsworth Math. Ser., Wadsworth, Belmont, Calif
    • N. Varopoulos, “Potential theory and diffusion on Riemannian manifolds” in Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. 2, Wadsworth Math. Ser., Wadsworth, Belmont, Calif., 1983, 821-837.
    • (1983) Conference on Harmonic Analysis in Honor of Antoni Zygmund , vol.2 , pp. 821-837
    • Varopoulos, N.1
  • 48
    • 0003858346 scopus 로고
    • Conformal Geometry and Quasiregular Mappings
    • Springer-Verlag, Berlin
    • M. Vuorinen, Conformal Geometry and Quasiregular Mappings, Lecture Notes in Math. 1319, Springer-Verlag, Berlin, 1988.
    • (1988) Lecture Notes in Math. 1319
    • Vuorinen, M.1
  • 49
    • 84980178548 scopus 로고
    • Harmonic functions on complete Riemannian manifolds
    • S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201-228.
    • (1975) Comm. Pure Appl. Math , vol.28 , pp. 201-228
    • Yau, S.T.1


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