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

Research paper by Christian Rose

Indexed on: 22 Jun '16Published on: 22 Jun '16Published in: Mathematics - Differential Geometry

#### 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.