Eigenvalues and entropys under the harmonic-Ricci flow

Details Eigenvalues and entropys under the harmonic-Ricci flow Eigenvalues and entropys under the harmonic-Ricci flow

2010-11-08

arxiv.org/abs/1011.1697v1

Mathematics

Differential Geometry

43 pages

Scientific paper

In this paper, the author discuss the eigenvalues and entropys 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 entropys of the harmonic-Ricci flow.

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