Heat kernel estimates on manifolds with ends with mixed boundary condition
Differential Geometry
2025-01-15 v2 Analysis of PDEs
Probability
Abstract
We obtain two-sided heat kernel estimates for Riemannian manifolds with ends with mixed boundary condition, provided that the heat kernels for the ends are well understood. These results extend previous results of Grigor'yan and Saloff-Coste by allowing for Dirichlet boundary condition. The proof requires the construction of a global harmonic function which is then used in the -transform technique.
Cite
@article{arxiv.2108.05790,
title = {Heat kernel estimates on manifolds with ends with mixed boundary condition},
author = {Emily Dautenhahn and Laurent Saloff-Coste},
journal= {arXiv preprint arXiv:2108.05790},
year = {2025}
}
Comments
35 pages, 9 figures