Volumetric density estimates for nonlocal minimal surfaces
Analysis of PDEs
2026-05-05 v1
Abstract
In this article, we prove that viscosity subsolutions to nonlocal mean curvature-type equations satisfy universal volumetric estimates at all scales. Our results hold for general symmetric kernels that are comparable to the fractional Laplacian. Furthermore, we prove that subsolutions with low density (with respect to a universal constant) necessarily have `fat boundary', that is, have topological boundary with positive Lebesgue measure.
Cite
@article{arxiv.2605.02176,
title = {Volumetric density estimates for nonlocal minimal surfaces},
author = {Mateusz Kwaśnicki and Jack Thompson},
journal= {arXiv preprint arXiv:2605.02176},
year = {2026}
}