Differential Harnack Estimates for Parabolic Equations

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.

10 pages

Cited by in corpus (2)

• Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
• Interpolating between constrained Li-Yau and Chow-Hamilton Harnack inequalities for a nonlinear parabolic equation