# On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces

created by ambrosio on 13 Sep 2013
modified by paolini on 19 Dec 2014

[BibTeX]

Accepted Paper

Inserted: 13 sep 2013
Last Updated: 19 dec 2014

Journal: Journal of Geometric Analysis
Year: 2014
Doi: 10.1007/s12220-014-9537-7

Abstract:

We prove higher summability and regularity of $\Gamma(f)$ for functions $f$ in spaces satisfying the Bakry-Èmery condition $BE(K,\infty)$.

As a byproduct, we obtain various equivalent weak formulations of $BE(K,N)$ and we prove the Local-to-Global property of the $RCD^*(K,N)$ condition in locally compact metric measure spaces $(X,d,m)$, without assuming a priori the non-branching condition on the metric space.

Tags: GeMeThNES