A rigidity result for metric measure spaces with Euclidean heat kernel

Gilles Carron; David Tewodrose

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arXiv · 1912.10759

A rigidity result for metric measure spaces with Euclidean heat kernel

Gilles Carron·David Tewodrose

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Abstract

We prove that a metric measure space equipped with a Dirichlet form admitting an Euclidean heat kernel is necessarily isometric to the Euclidean space. This helps us providing an alternative proof of Colding's celebrated almost rigidity volume theorem via a quantitative version of our main result. We also discuss the case of a metric measure space equipped with a Dirichlet form admitting a spherical heat kernel.

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Gilles Carron, David Tewodrose. 2019-12-23. A rigidity result for metric measure spaces with Euclidean heat kernel. https://arxiv.org/abs/1912.10759

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