Harnack inequalities and $W$-entropy formula for Witten Laplacian on Riemannian manifolds with $K$-super Perelman Ricci flow

Songzi Li, Xiang-Dong Li

In this paper, we prove logarithmic Sobolev inequalities and derive the Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on complete Riemannian manifolds…