Geometric heat comparison criteria for Riemannian manifolds
Leon Karp (City University of New York), Norbert Peyerimhoff, (University of Durham)
TL;DR
This paper establishes small-time heat comparison criteria for points in Riemannian manifolds using geometric measures like distance and spherical area, with applications illustrated through examples.
Contribution
It introduces new small-time heat comparison results on Riemannian manifolds based on geometric concepts such as distance from the complement and spherical area functions.
Findings
Heat comparison results for two points in manifolds
Use of geometric functions for heat analysis
Illustrative examples demonstrating the results
Abstract
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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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Numerical methods in inverse problems · Nonlinear Partial Differential Equations