Heat kernel estimates under the Ricci-Harmonic map flow
Differential Geometry
2013-10-08 v1
Abstract
The paper considers the Ricci flow, coupled with the harmonic map flow between two manifolds. We derive estimates for the fundamental solution of the corresponding conjugate heat equation and we prove an analog of Perelman's differential Harnack inequality. As an application, we find a connection between the entropy functional and the best constant in the Sobolev imbedding theorem in .
Cite
@article{arxiv.1310.1619,
title = {Heat kernel estimates under the Ricci-Harmonic map flow},
author = {Mihai Băileşteanu and Hung Tran},
journal= {arXiv preprint arXiv:1310.1619},
year = {2013}
}
Comments
23 pages. arXiv admin note: substantial text overlap with arXiv:1309.0138, arXiv:1010.5543