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Geometric Heat Comparison Criteria for Riemannian Manifolds

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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.

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Authors and Affiliations

  1. Department of Mathematics, CUNY Graduate Center and Lehman College, 365 Fifth Avenue, New York, NY, 10016, USA

    Leon Karp

  2. Department of Mathematical Sciences, Durham University, South Road, Durham, DH1 3LE, United Kingdom

    Norbert Peyerimhoff

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  1. Leon Karp
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  2. Norbert Peyerimhoff
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Correspondence to Norbert Peyerimhoff.

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Mathematics subject classifications (2000): 58J35, 35K05

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Karp, L., Peyerimhoff, N. Geometric Heat Comparison Criteria for Riemannian Manifolds. Ann Glob Anal Geom 31, 115–145 (2007). https://doi.org/10.1007/s10455-006-9038-4

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  • DOI: https://doi.org/10.1007/s10455-006-9038-4

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