English

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 Rn\mathbb{R}^n.

Keywords

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

R2 v1 2026-06-22T01:41:18.969Z