An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces
Abstract
In this work, we establish a new characterization of sub-Gaussian heat kernel estimates for strongly local regular Dirichlet forms on metric measure spaces. Our formulation is based on the newly introduced cutoff energy condition, which offers a simpler and more transparent alternative for earlier technical energy inequalities, in particular the cutoff Sobolev inequality. The main idea of our approach is to reinterpret the cutoff Sobolev inequality as a Poincar\'e type inequality, and analyze it using Haj{\l}asz--Koskela techniques from analysis on metric spaces. Applications of the new characterization are also discussed.
Keywords
Cite
@article{arxiv.2509.04155,
title = {An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces},
author = {Riku Anttila},
journal= {arXiv preprint arXiv:2509.04155},
year = {2025}
}
Comments
37 pages, comments are welcome! Revision: The main results have been generalized to cover cases where the ambient space is not necessarily geodesic. A brief discussion on applications to reflected diffusion has been included