Spectral Bounds and Heat Kernel Upper Estimates for Dirichlet Forms
Abstract
ABSTRACT We use a Harnack‐type inequality on exit times and spectral bounds to characterize upper bounds of the heat kernel associated with any regular Dirichlet form without killing part, where the scale function may vary with position. We further show that this Harnack‐type inequality is preserved under quasi‐symmetric changes of metric on uniformly perfect metric spaces. This generalizes the work of Mariano and Wang [ Stochastic Process. Appl . 189 (2025): 104707].
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Mathematische Nachrichten
- Volume
- 299
- Issue
- 9
- Pages
- 2566–2589
- Publication date
- 11 August 2026
- Language
- EN