Unbounded mean convex domains in Euclidean space

TL;DR

This paper proves that for any disconnected boundary of an unbounded mean convex domain in Euclidean space, the lowest mean curvature on each boundary component is zero.

Contribution

It establishes a fundamental property of mean convex domains, showing the infimum of mean curvature on disconnected boundary components is always zero.

Findings

The infimum of mean curvature on disconnected boundary components is zero.

This property holds for unbounded mean convex domains in any Euclidean space.

The result clarifies geometric constraints on such domains.

Abstract

In this note, we prove that the infimum of the mean curvature on any disconnected boundary component of an unbounded mean convex domain in $\mathbb{R}^n$ must be zero.