Geometric Heat Comparison Criteria for Riemannian Manifolds |
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| Authors: | Leon Karp Norbert Peyerimhoff |
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| Institution: | (1) Department of Mathematics, CUNY Graduate Center and Lehman College, 365 Fifth Avenue, New York, NY 10016, USA;(2) Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom |
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| Abstract: | The main results of this paper 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.
Mathematics subject classifications (2000): 58J35, 35K05 |
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| Keywords: | Heat equation Riemannian manifolds Geometric comparison results |
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