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The Li-Yau inequality and applications under a curvature-dimension condition

Abstract : We prove a global Li-Yau inequality for a general Markov semigroup under a curvature-dimension condition. This inequality is stronger than all classical Li-Yau type inequalities known to us. On a Riemannian manifold, it is equivalent to a new parabolic Harnack inequality, both in negative and positive curvature, giving new subsequents bounds on the heat kernel of the semigroup. Under positive curvature we moreover reach ultracontractive bounds by a direct and robust method.
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https://hal.archives-ouvertes.fr/hal-01094046
Contributor : Ivan Gentil <>
Submitted on : Thursday, July 21, 2016 - 12:54:06 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:57 PM

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Distributed under a Creative Commons Attribution - NonCommercial 4.0 International License

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  • HAL Id : hal-01094046, version 3
  • ARXIV : 1412.5165

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Dominique Bakry, François Bolley, Ivan Gentil. The Li-Yau inequality and applications under a curvature-dimension condition. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, 2017, 67 (1), pp.397-421. ⟨hal-01094046v3⟩

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