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arXiv · 1001.5245

Differential Harnack Estimates for Parabolic Equations

Xiaodong Cao·Zhou Zhang
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Abstract

Let $(M,g(t))$ be a solution to the Ricci flow on a closed Riemannian manifold. In this paper, we prove differential Harnack inequalities for positive solutions of nonlinear parabolic equations of the type $$\ppt f=Δf-f \ln f +Rf.$$ We also comment on an earlier result of the first author on positive solutions of the conjugate heat equation under the Ricci flow.

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Xiaodong Cao, Zhou Zhang. 2010-01-28. Differential Harnack Estimates for Parabolic Equations. https://arxiv.org/abs/1001.5245

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