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arXiv · 1009.1219

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

Jia-Yong Wu
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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 $\varepsilon$-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.

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Jia-Yong Wu. 2010-09-07. Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow. https://doi.org/10.2140/pjm.2012.257.199

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