Nonlocal minimal surfaces: interior regularity, quantitative estimates and boundary stickiness

TL;DR

This paper studies nonlocal minimal surfaces, focusing on their interior regularity, boundary behavior, and quantitative estimates, providing elementary and self-contained proof sketches.

Contribution

It offers new insights into the regularity and boundary properties of nonlocal minimal surfaces with elementary proof approaches.

Findings

Interior regularity of nonlocal minimal surfaces

Quantitative estimates of boundary behavior

Rigidity properties of these surfaces

Abstract

We consider surfaces which minimize a nonlocal perimeter functional and we discuss their interior regularity and rigidity properties, in a quantitative and qualitative way, and their (perhaps rather surprising) boundary behavior. We present at least a sketch of the proofs of these results, in a way that aims to be as elementary and self contained as possible.