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Manifolds and graphs with slow heat kernel decay

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Inventiones mathematicae Aims and scope

Abstract.

We give upper estimates on the long time behavior of the heat kernel on non-compact Riemannian manifolds and infinite graphs, which only depend on a lower bound of the volume growth. We also show that these estimates are sharp.

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Authors and Affiliations

  1. University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada (e-mail: barlow@math.ubc.ca), , , , , , CA

    Martin Barlow

  2. Université de Cergy-Pontoise, 95302 Pontoise, France (e-mail: Thierry.Coulhon@math.u-cergy.fr), , , , , , FR

    Thierry Coulhon

  3. Imperial College, London SW7 2BZ, United Kingdom (e-mail: a.grigoryan@ic.ac.uk), , , , , , GB

    Alexander Grigor’yan

Authors
  1. Martin Barlow
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  2. Thierry Coulhon
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  3. Alexander Grigor’yan
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Additional information

Oblatum 23-VIII-1999 & 21-XII-2000¶Published online: 5 March 2001

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Barlow, M., Coulhon, T. & Grigor’yan, A. Manifolds and graphs with slow heat kernel decay. Invent. math. 144, 609–649 (2001). https://doi.org/10.1007/s002220100139

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  • DOI: https://doi.org/10.1007/s002220100139

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