Geometric heat comparison criteria for Riemannian manifolds

Details Geometric heat comparison criteria for Riemannian manifolds Geometric heat comparison criteria for Riemannian manifolds

2005-06-10

arxiv.org/abs/math-ph/0506023v1

Physics

Mathematical Physics

28 pages, 10 figures. See also http://maths.dur.ac.uk/pure/preprint.html

Scientific paper

The main results of this article are small time heat comparison results for two points in two manifolds with characteristic functions as initial temperature distributions (Theorems 1 and 2). These results are based on the geometric concepts of (essential) distance from the complement and spherical area function. We also discuss some other geometric results about the heat development and illustrate them by examples.

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