On the Bakry-Èmery condition, the gradient estimates and the Local-to-Global property of $RCD^*(K,N)$ metric measure spaces
Journal of Geometric Analysis
We prove higher summability and regularity of
$\Gamma(f)$ for functions $f$ in spaces satisfying the Bakry-Èmery condition
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.
The paper is available on the
cvgmt preprint server.