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arXiv · 1011.1697

Eigenvalues and entropies under the harmonic-Ricci flow

Yi Li
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Abstract

In this paper, the author discusses the eigenvalues and entropies under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for compact steady and expanding harmonic-Ricci breathers. In the second part, we derive some monotonicity formulas for eigenvalues of Laplacian under the harmonic-Ricci flow. Finally, we obtain the first variation of the shrinker and expanding entropies of the harmonic-Ricci flow.

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Yi Li. 2010-11-08. Eigenvalues and entropies under the harmonic-Ricci flow. https://doi.org/10.2140/pjm.2014.267.141

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