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Updated: Aug 13, 2025

Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Pointwise monotonicity of heat kernels
Diego Alonso-Orán1, Fernando Chamizo2, Ángel D Martínez2
1Institute für Angewandte Mathematik, Universitat Bonn, Endenicher Allee 60, Bonn, 53115 Germany.
Abstract:
In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.
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