English

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 hh-transform technique.

Keywords

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

R2 v1 2026-06-24T05:04:09.349Z