Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds
Differential Geometry
2015-10-20 v1
Abstract
In this article we derive Harnack estimates for conjugate heat kernel in an abstract geometric flow. Our calculation involves a correction term D. When D is nonnegative, we are able to obtain a Harnack inequality. Our abstract formulation provides a unified framework for some known results, in particular including corresponding results of Ni, Perelman, and Tran as special cases. Moreover it leads to new results in the setting of Ricci-Harmonic flow and mean curvature flow in Lorentzian manifolds with nonnegative sectional curvature.
Cite
@article{arxiv.1408.4155,
title = {Harnack Estimates for Conjugate Heat Kernel on Evolving Manifolds},
author = {Xiaodong Cao and Hongxin Guo and Hung Tran},
journal= {arXiv preprint arXiv:1408.4155},
year = {2015}
}
Comments
16p