Published Paper

Inserted: 19 nov 2020
Last Updated: 24 feb 2022

Journal: Journal de l'École Polytechnique --- Mathématiques
Volume: 9
Pages: 101-154
Year: 2022

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.