Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow

Abstract

We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the $\epsilon$-Ricci flow on a closed surface. These new Harnack inequalities extend the previous differential Harnack inequalities for linear heat equations with potentials under the Ricci flow.

17 pages. New explanations added; Final version

References in corpus (7)

• Gradient estimates for the heat equation under the Ricci flow
• Gradient estimates for a nonlinear parabolic equation under Ricci flow
• Gradient estimates for a nonlinear diffusion equation on complete manifolds
• Hamilton type estimates for heat equations on manifolds
• Differential Harnack Estimates for Parabolic Equations
• Differential Harnack Estimates for Backward Heat Equations with Potentials under the Ricci Flow
• Gradient estimates for a simple nonlinear heat equation on manifolds

Cited by in corpus (4)

• Harnack Estimates for Nonlinear Backward Heat Equations in Geometric Flows
• Harnack Estimates for Nonlinear Heat Equations with Potentials in Geometric Flows
• Interpolating between constrained Li-Yau and Chow-Hamilton Harnack inequalities for a nonlinear parabolic equation
• New differential Harnack inequalities for nonlinear heat equations