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

2016/08/15 by Rose, Christian · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.04221

Abstract

This article shows that if the negative part of Ricci curvature lies in the Kato class, the heat kernel satisfies a Li-Yau type estimate. Additionally, using the resulting heat kernel bound, we show that the obtained heat kernel estimate leads to bounds on the first Betti number only depending on the Kato constant.

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• Comparison estimates on nonsmooth spaces with integrable Ricci lower bounds via localization

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