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


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.


Heat kernel Ricci curvature Kato class 


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© Springer Nature B.V. 2018

Authors and Affiliations

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

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