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



Autor: Yi Li

Fuente: https://arxiv.org/







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