Heat kernel estimates under the Ricci-Harmonic map flow

Mihai Băileşteanu; Hung Tran

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arXiv · 1310.1619

Heat kernel estimates under the Ricci-Harmonic map flow

Mihai Băileşteanu·Hung Tran

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Abstract

The paper considers the Ricci flow, coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analog of Perelman's differential Harnack inequality. As an application, we find a connection between the entropy functional and the best constant in the Sobolev imbedding theorem in $\mathbb{R}^n$.

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BibTeX RIS

Mihai Băileşteanu, Hung Tran. 2013-10-06. Heat kernel estimates under the Ricci-Harmonic map flow. https://arxiv.org/abs/1310.1619

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