Eigenvalues and entropies under the harmonic-Ricci flow
Differential Geometry
2016-01-20 v2
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.
Keywords
Cite
@article{arxiv.1011.1697,
title = {Eigenvalues and entropies under the harmonic-Ricci flow},
author = {Yi Li},
journal= {arXiv preprint arXiv:1011.1697},
year = {2016}
}
Comments
37 pages; final version to appear in Pacific J. Math