Abstract
In this paper, we prove the Hamilton differential Harnack inequality for positive solutions to the heat equation of the Witten Laplacian on complete Riemannian manifolds with the CD(−K,m)-condition, where m∈[n,∞) and K≥0 are two constants. Moreover, we introduce the W-entropy and prove the W-entropy formula for the fundamental solution of the Witten Laplacian on complete Riemannian manifolds with the CD(−K,m)-condition and on compact manifolds equipped with (−K,m)-super Ricci flows.
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