A note on heat kernel estimates, resistance bounds and Poincaré inequality

2018/09/04 by Mathav Murugan, Murugan, Mathav · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1809.00767

openalex publication_date 2018/09/04 · openalex created_date 2018/09/27 · openalex updated_date 2026/07/28

Abstract

Sub-Gaussian heat kernel estimates are typical of fractal graphs. We show that sub-Gaussian estimates on graphs follow from a Poincaré inequality, capacity upper bound, and a slow volume growth condition. An important feature of this work is that we do not assume elliptic Harnack inequality, cutoff Sobolev inequality, or exit time bounds.

Citations

• Quasiconformal maps in metric spaces with controlled geometry

Cited by

• An approach to sub-Gaussian heat kernel estimates via analysis on metric spaces
• Energy inequalities for cutoff functions of p-energies on metric measures spaces

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