# Self-improvement of gradient estimate of heat flows on metric measure spaces

created by han1 on 22 Oct 2017

[BibTeX]

preprint

Inserted: 22 oct 2017
Last Updated: 22 oct 2017

Year: 2017

ArXiv: 1702.00740 PDF

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.