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arXiv · 1309.0139

Gradient estimates for the heat equation under the Ricci-Harmonic Map flow

Mihai Băileşteanu
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Abstract

The paper establishes a series of gradient estimates for positive solutions to the heat equation on a manifold $M$ evolving under the Ricci flow, coupled with the harmonic map flow between $M$ and a second manifold $N$. We prove Li-Yau type Harnack inequalities and we consider the cases when $M$ is a complete manifold without boundary and when $M$ is compact, without boundary.

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Mihai Băileşteanu. 2013-08-31. Gradient estimates for the heat equation under the Ricci-Harmonic Map flow. https://doi.org/10.1515/advgeom-2015-0028

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