Calculus of Variations and Geometric Measure Theory
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G. Carron - D. Tewodrose

A rigidity result for metric measure spaces with Euclidean heat kernel

created by tewodrose on 19 Nov 2020

[BibTeX]

Submitted Paper

Inserted: 19 nov 2020
Last Updated: 19 nov 2020

Year: 2019

ArXiv: 1912.10759 PDF

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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