Hamilton's Harnack inequality and the W-entropy formula on complete Riemannian manifolds
classification
🧮 math.PR
keywords
completemanifoldsproveriemannianentropyformulahamiltonharnack
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In this paper, we prove Hamilton's Harnack inequality and the gradient estimates of the logarithmic heat kernel for the Witten Laplacian on complete Riemainnian manifolds. As applications, we prove the $W$-entropy formula for the Witten Laplacian on complete Riemannian manifolds, and prove a family of logarithmic Sobolev inequalities on complete Riemannian manifolds with natural geometric condition.
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