Rotational symmetry of self-expanders to the inverse mean curvature flow with cylindrical ends

TL;DR

This paper proves that complete self-expanders to the inverse mean curvature flow with cylindrical ends are necessarily rotationally symmetric, revealing a symmetry property under specific asymptotic conditions.

Contribution

It establishes the rotational symmetry of self-expanders with cylindrical ends, a new geometric characterization in inverse mean curvature flow.

Findings

Self-expanders with one cylindrical end are rotationally symmetric.

Self-expanders with two coaxial cylindrical ends are rotationally symmetric.

The symmetry result applies to complete, immersed self-expanders under the given asymptotic conditions.

Abstract

We show that any complete, immersed self-expander to the inverse mean curvature flow, which has one end asymptotic to a cylinder, or has two ends asymptotic to two coaxial cylinders, must be rotationally symmetric.