Pointwise monotonicity of heat kernels
Classical Analysis and ODEs
2019-05-28 v2 Analysis of PDEs
Abstract
In this paper the authors present a proof of a pointwise radial monotonicity property of heat kernels that is shared by the euclidean spaces, spheres and hyperbolic spaces. The main result deals with monotonicity from special points on revolution hypersurfaces from which the aforementioned are deduced. The proof relies on a non straightforward but elementary application of the parabolic maximum principle.
Cite
@article{arxiv.1807.11072,
title = {Pointwise monotonicity of heat kernels},
author = {Diego Alonso-Orán and Fernando Chamizo and Ángel D. Martínez and Albert Mas},
journal= {arXiv preprint arXiv:1807.11072},
year = {2019}
}