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Volumn 6, Issue 3-4, 1999, Pages 307-321

Heat kernel on connected sums of Riemannian manifolds

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EID: 0033245886     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/MRL.1999.v6.n3.a5     Document Type: Article
Times cited : (25)

References (23)
  • 2
    • 0000241904 scopus 로고    scopus 로고
    • Heat kernel lower bounds on Riemannian manifolds using the old ideas of Nash
    • [2] I. Benjamini, I. Chavel, and E.A. Feldman, Heat kernel lower bounds on Riemannian manifolds using the old ideas of Nash, Proc. London Math. Soc. (3) 72 (1996) 215-240.
    • (1996) Proc. London Math. Soc. , vol.72 , Issue.3 , pp. 215-240
    • Benjamini, I.1    Chavel, I.2    Feldman, E.A.3
  • 3
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • [3] 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
  • 4
    • 84980136552 scopus 로고
    • A lower bound for the heat kernel
    • [4] J. Cheeger and S.-T. Yau, A lower bound for the heat kernel, Comm. Pure Appl. Math. 34 (1981) 465-480.
    • (1981) Comm. Pure Appl. Math. , vol.34 , pp. 465-480
    • Cheeger, J.1    Yau, S.-T.2
  • 5
    • 84980189206 scopus 로고
    • Differential equations on Riemannian manifolds and their geometric applications
    • [5] 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
  • 6
    • 0001565149 scopus 로고    scopus 로고
    • On-diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains
    • [6] T. Coulhon and A. Grigor'yan, On-diagonal lower bounds for heat kernels on non-compact manifolds and Markov chains, Duke Math. J. 89 (1997) 133-199.
    • (1997) Duke Math. J. , vol.89 , pp. 133-199
    • Coulhon, T.1    Grigor'yan, A.2
  • 7
    • 0001683890 scopus 로고
    • Explicit constants for Gaussian upper bounds on heat kernels
    • [7] E.B. Davies, Explicit constants for Gaussian upper bounds on heat kernels, Amer. J. Math. 109 (1987) 319-334.
    • (1987) Amer. J. Math. , vol.109 , pp. 319-334
    • Davies, E.B.1
  • 8
    • 0000960981 scopus 로고
    • Gaussian upper bounds for the heat kernel of some second-order operators on Riemannian manifolds
    • [8] -, Gaussian upper bounds for the heat kernel of some second-order operators on Riemannian manifolds, J. Funct. Anal. 80 (1988) 16-32.
    • (1988) J. Funct. Anal. , vol.80 , pp. 16-32
  • 9
    • 0001563743 scopus 로고    scopus 로고
    • Non-Gaussian aspects of heat kernel behaviour
    • [9] -, Non-Gaussian aspects of heat kernel behaviour, J. London Math. Soc. (2) 55 (1997) 105-125.
    • (1997) J. London Math. Soc. , vol.55 , Issue.2 , pp. 105-125
  • 10
    • 0000123369 scopus 로고
    • On the existence of positive fundamental solution of the Laplace equation on Riemannian manifolds
    • Russian
    • [10] A. Grigor'yan, On the existence of positive fundamental solution of the Laplace equation on Riemannian manifolds, (Russian) Mat. Sb. (N.S.) 128 (1985) 354-363. Engl. transl. in Math. USSR Sb. 56 (1987) 349-358.
    • (1985) Mat. Sb. (N.S.) , vol.128 , pp. 354-363
    • Grigor'yan, A.1
  • 11
    • 84956133692 scopus 로고
    • [10] A. Grigor'yan, On the existence of positive fundamental solution of the Laplace equation on Riemannian manifolds, (Russian) Mat. Sb. (N.S.) 128 (1985) 354-363. Engl. transl. in Math. USSR Sb. 56 (1987) 349-358.
    • (1987) Math. USSR Sb. , vol.56 , pp. 349-358
  • 12
    • 0002209819 scopus 로고
    • The heat equation on non-compact Riemannian manifolds
    • Russian
    • [11] A. Grigor'yan, The heat equation on non-compact Riemannian manifolds,(Russian) Matem. Sbornik 182 (1991) 55-87. Engl. transl. in Math. USSR Sb. 72 (1992) 47-77.
    • (1991) Matem. Sbornik , vol.182 , pp. 55-87
    • Grigor'yan, A.1
  • 13
    • 84956103754 scopus 로고
    • [11] A. Grigor'yan, The heat equation on non-compact Riemannian manifolds,(Russian) Matem. Sbornik 182 (1991) 55-87. Engl. transl. in Math. USSR Sb. 72 (1992) 47-77.
    • (1992) Math. USSR Sb. , vol.72 , pp. 47-77
  • 14
    • 0001436849 scopus 로고
    • Heat kernel upper bounds on a complete non-compact manifold
    • [12] -, Heat kernel upper bounds on a complete non-compact manifold, Rev. Mat. Iberoamericana 10 (1994) 395-452.
    • (1994) Rev. Mat. Iberoamericana , vol.10 , pp. 395-452
  • 15
    • 0039657135 scopus 로고    scopus 로고
    • Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
    • [13] -, Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds, Bull. Amer. Math. Soc. (N.S.) 36 (1999) 135-249.
    • (1999) Bull. Amer. Math. Soc. (N.S.) , vol.36 , pp. 135-249
  • 16
    • 0003245243 scopus 로고
    • Subharmonic functions, harmonic mappings and isometric immersions
    • Seminar on Differential Geometry, (S.T. Yau, ed.) Princeton University Press, Princeton, N.J.
    • [14] L. Karp, Subharmonic functions, harmonic mappings and isometric immersions, Seminar on Differential Geometry, (S.T. Yau, ed.) Ann. Math. Stud. 102, Princeton University Press, Princeton, N.J., 1982.
    • (1982) Ann. Math. Stud. , vol.102
    • Karp, L.1
  • 17
    • 0009240239 scopus 로고
    • Counterexamples to Liouville-type theorems
    • Russian
    • [15] Yu.T. Kuz'menko and S.A. Molchanov, Counterexamples to Liouville-type theorems, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1979) 39-43. Engl. transl. in Moscow Univ. Math. Bull. 34 (1979) 35-39.
    • (1979) Vestnik Moskov. Univ. Ser. I Mat. Mekh. , pp. 39-43
    • Kuz'menko, Yu.T.1    Molchanov, S.A.2
  • 18
    • 0009096745 scopus 로고
    • [15] Yu.T. Kuz'menko and S.A. Molchanov, Counterexamples to Liouville-type theorems, (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1979) 39-43. Engl. transl. in Moscow Univ. Math. Bull. 34 (1979) 35-39.
    • (1979) Moscow Univ. Math. Bull. , vol.34 , pp. 35-39
  • 19
    • 0000324115 scopus 로고
    • On the parabolic kernel of the Schrödinger operator
    • [16] P. Li and S.-T. Yau, On the parabolic kernel of the Schrödinger operator, Acta Math. 156 (1986) no.3-4, 153-201.
    • (1986) Acta Math. , vol.156 , Issue.3-4 , pp. 153-201
    • Li, P.1    Yau, S.-T.2
  • 21
    • 84972525827 scopus 로고
    • Uniformly elliptic operators on Riemannian manifolds
    • [18] -, Uniformly elliptic operators on Riemannian manifolds, J. Diff. Geom. 36 (1992) 417-450.
    • (1992) J. Diff. Geom. , vol.36 , pp. 417-450
  • 23
    • 0001598968 scopus 로고
    • Potential theory and diffusion of Riemannian manifolds
    • Wadsworth Math. Ser., Wadsworth, Belmont, Calif.
    • [20] N.Th. Varopoulos, Potential theory and diffusion of Riemannian manifolds, Conference on Harmonic Analysis in honor of Antoni Zygmund. Vol I, II., pp. 821-837, Wadsworth Math. Ser., Wadsworth, Belmont, Calif., 1983.
    • (1983) Conference on Harmonic Analysis in Honor of Antoni Zygmund , vol.1-2 , pp. 821-837
    • Varopoulos, N.Th.1


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