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Mathematische Annalen

, Volume 292, Issue 1, pp 149–162 | Cite as

Heat kernel bounds on manifolds

  • Karl-Theodor Sturm
Article

Keywords

Manifold Heat Kernel Kernel Bound Heat Kernel Bound 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Chavel, I.: Eigenvalues in Riemannian geometry. Boston: Academic Press 1984Google Scholar
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    Cheeger, J., Yau, S.T.: A lower bound for the heat kernel Commun. Pure Appl. Math.34, 465–480 (1981)Google Scholar
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    Davies, E.B.: Gaussian upper bounds for the heat kernel of some second-order operators on Riemannian manifolds. J. Funct. Anal.80, 16–32 (1988)Google Scholar
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    Davies, E.B.: Heat kernels and spectral theory. Cambridge: Cambridge University Press 1989Google Scholar
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    Davies, E.B., Mandouvalos, N.: Heat kernel bounds on hyperbolic space and Kleinian groups. Proc. Lond. Math. Soc.57, 182–208 (1988)Google Scholar
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    Debiard, A., Gaveau, B., Mazet, E.: Théorèmes de comparaisons en géométrie Riemannienne. Publ. Res. Inst. Math. Sci.12, 391–425 (1976)Google Scholar
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    Gallot, S., Hulin, D., Lafontaine, J.: Riemannian geometry. Berlin Heidelberg New York: Springer 1987Google Scholar
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    Li, P., Yau, S.T.: On the parabolic kernel of the Schrödinger operator. Acta Math.156, 153–201 (1986)Google Scholar
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    Sturm, K.-Th.: Schrödinger semigroups on manifolds. (Preprint, Erlangen 1990)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Karl-Theodor Sturm
    • 1
  1. 1.Mathematisches InstitutUniversität ErlangenErlangenFederal Republic of Germany

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