Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds

2016/01/27 by Rose, Christian
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.07438

Abstract

This article shows that under locally uniformly integral bounds of the negative part of Ricci curvature the heat kernel admits a Gaussian upper bound for small times. This provides general assumptions on the geometry of a manifold such that certain function spaces are in the Kato class. Additionally, the results imply bounds on the first Betti number.

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