Stability of elliptic Harnack inequality

TL;DR

This paper demonstrates that the elliptic Harnack inequality remains stable under bounded perturbations and rough isometries across various geometric settings such as manifolds, graphs, and metric measure spaces.

Contribution

It establishes the stability of the elliptic Harnack inequality under bounded perturbations and rough isometries, extending its applicability.

Findings

Harnack inequality is stable under bounded perturbations.

Stability also holds under rough isometries.

Results apply to manifolds, graphs, and metric measure spaces.

Abstract

We prove that the elliptic Harnack inequality (on a manifold, graph, or suitably regular metric measure space) is stable under bounded perturbations, as well as rough isometries.