Heat Kernel for Open Manifolds

Trevor H. Jones

doi:10.1016/j.difgeo.2010.02.003

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arXiv · 0910.4539

Heat Kernel for Open Manifolds

Trevor H. Jones

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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 $k$.

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Trevor H. Jones. 2009-10-23. Heat Kernel for Open Manifolds. https://doi.org/10.1016/j.difgeo.2010.02.003

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