Eigenvalues and entropies under the harmonic-Ricci flow
arXiv:1011.1697 · doi:10.2140/pjm.2014.267.141
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.
37 pages; final version to appear in Pacific J. Math