A half-space theorem for nonlocal minimal surfaces

TL;DR

This paper proves a half-space theorem for nonlocal minimal surfaces, extending classical results to all dimensions, highlighting differences from traditional minimal surface theory.

Contribution

It introduces a half-space theorem for nonlocal minimal surfaces that applies universally across dimensions, unlike classical results.

Findings

The theorem holds in every dimension.

It distinguishes nonlocal minimal surfaces from classical ones.

The result generalizes classical half-space theorems.

Abstract

We establish a half-space theorem \`a la Hoffman and Meeks for nonlocal minimal surfaces. Differently from the classical case, our result holds in every dimension.