English

Davies type estimate and the heat kernel bound under the Ricci flow

Differential Geometry 2014-02-11 v2 Analysis of PDEs

Abstract

We prove a Davies type double integral estimate for the heat kernel H(y,t;x,l)H(y,t;x,l) under the Ricci flow. As a result, we give an affirmative answer to a question proposed by Chow etc.. Moreover, we apply the Davies type estimate to provide a new proof of the Gaussian upper and lower bounds of H(y,t;x,l)H(y,t;x,l) which were first shown by Chau-Tam-Yu.

Keywords

Cite

@article{arxiv.1311.5950,
  title  = {Davies type estimate and the heat kernel bound under the Ricci flow},
  author = {Meng Zhu},
  journal= {arXiv preprint arXiv:1311.5950},
  year   = {2014}
}

Comments

conditions refined, some errors corrected