On the $W$-entropy and Shannon entropy power on RCD$(K,N)$ and RCD$(K,n,N)$ spaces

Xiang-Dong Li, Enrui Zhang

In this paper, we prove the $W$-entropy formula and the monotonicity and rigidity theorem of the $W$-entropy for the heat flow on RCD$(K,N)$ and RCD$(K,n,N)$ spaces $(X,d,\hat{I}¼)$…