Key points are not available for this paper at this time.
In this paper, we prove the Li-Yau type Harnack inequality and Hamilton type dimension free Harnack inequality for the heat equation ₜ u=Lu associated with the time dependent Witten Laplacian on complete Riemannian manifolds equipped with a variant of the (K, m) -super Perelman Ricci flows and the K-super Perelman Ricci flows.
Li et al. (Mon,) studied this question.