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OFF-DIAGONAL HEAT KERNEL LOWER BOUNDS WITHOUT POINCARÉ

  • THIERRY COULHON (a1)
Abstract

On a manifold with polynomial volume growth satisfying Gaussian upper bounds of the heat kernel, a simple characterization of the matching lower bounds is given in terms of a certain Sobolev inequality. The method also works in the case of so-called sub-Gaussian or sub-diffusive heat kernels estimates, which are typical of fractals. Together with previously known results, this yields a new characterization of the full upper and lower Gaussian or sub-Gaussian heat kernel estimates.

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Research partially supported by the European Commission (IHP Network ‘Harmonic analysis and related problems’ 2002–2006, contract HPRN-CT-2001-00273-HARP).
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Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
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