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

Christian Rose

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arXiv · 1601.07438

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

Christian Rose

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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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BibTeX RIS

Christian Rose. 2016-06-22. Heat kernel upper bound on Riemannian manifolds with locally uniform Ricci curvature integral bounds. https://arxiv.org/abs/1601.07438

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