New characterizations of Ricci curvature on RCD metric measure spaces
New characterizations of Ricci curvature on RCD metric measure spaces
We prove that on a large family of metric measure spaces, if the $L^p$-gradient estimate for heat flows holds for some $p>2$, then the $L^1$-gradient estimate also holds. This result extends Savaré's result on metric measure spaces, and provides a new proof to von Renesse-Sturm theorem on smooth metric measure …