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.
| Original language | English |
|---|---|
| Pages (from-to) | 101-154 |
| Number of pages | 54 |
| Journal | Journal de l'Ecole Polytechnique - Mathematiques |
| Volume | 9 |
| DOIs | |
| Publication status | Published - 2021 |
Bibliographical note
Funding Information:G.C. was partially supported by the ANR grants ANR-17-CE40-0034 (CCEM) and ANR-18-CE40-0012(RAGE)..
Publisher Copyright:
© 2021 Ecole Polytechnique. All rights reserved.
Keywords
- Asymptotic cone
- Harmonic functions
- Heat kernel
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