On monotonicity of heat kernels: a new example and counterexamples
Differential Geometry
2025-02-13 v1 Analysis of PDEs
Classical Analysis and ODEs
Abstract
We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity property. Furthermore, we show that for a generic metric on any smooth manifold the monotonicity property fails at large times. This answers a recent question of Alonso-Or\'an, Chamizo, Mart\'inez, and Mas.
Keywords
Cite
@article{arxiv.2502.08212,
title = {On monotonicity of heat kernels: a new example and counterexamples},
author = {Almut Burchard and Ángel D. Martínez},
journal= {arXiv preprint arXiv:2502.08212},
year = {2025}
}