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Annals of Global Analysis and Geometry

, Volume 55, Issue 3, pp 443–449 | Cite as

Li–Yau gradient estimate for compact manifolds with negative part of Ricci curvature in the Kato class

  • Christian RoseEmail author
Article
  • 95 Downloads

Abstract

We show that a heat kernel estimate holds based on a Kato-class condition for the negative part of Ricci curvature. This is a generalization of results based on \(L^p\)-bounds on the Ricci curvature. We also establish bounds on the first Betti number.

Keywords

Heat kernel Ricci curvature Kato class 

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Max-Planck Institute for Mathematics in the SciencesLeipzigGermany

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