Heat Kernel for Open Manifolds
Differential Geometry
2010-08-02 v1 Analysis of PDEs
Abstract
In a 1991 paper by Buttig and Eichhorn, the existence and uniqueness of a differential forms heat kernel on open manifolds of bounded geometry was proven. In that paper, it was shown that the heat kernel obeyed certain properties, one of which was a relationship between the derivative of heat kernel of different degrees. We will give a proof of this condition for complete manifolds with Ricci curvature bounded below, and then use it to give an integral representation of the heat kernel of degree .
Cite
@article{arxiv.0910.4539,
title = {Heat Kernel for Open Manifolds},
author = {Trevor H. Jones},
journal= {arXiv preprint arXiv:0910.4539},
year = {2010}
}