Published Paper

Inserted: 22 oct 2017
Last Updated: 29 sep 2024

Journal: Discrete and Continuous Dynamical Systems
Year: 2018

Abstract:

We prove that on a large family of metric measure spaces, if the `carre du champ' $\Gamma$ satisfies a $p$-gradient estimate of heat flows for some $p>2$, then the metric measure space is ${\rm RCD}(K,\infty)$. The argument relies on the non-smooth Bakry-Emery's theory. As an application, we provide another proof of the von Renesse-Sturm's theorem on smooth metric measure space.

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• selfimprovement.pdf
• 6. @DCDS18@New characterizations of Ricci curvature on RCD metric measure spaces.pdf