Heat Kernel for Open Manifolds

Details Heat Kernel for Open Manifolds Heat Kernel for Open Manifolds

2009-10-23

arxiv.org/abs/0910.4539v1

Mathematics

Differential Geometry

Scientific paper

10.1016/j.difgeo.2010.02.003

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 $k$.

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