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arXiv · 2509.04155

An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces

Riku Anttila
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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.

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Riku Anttila. 2025-09-04. An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces. https://arxiv.org/abs/2509.04155

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