Embedded minimal and constant mean curvature annulus touching spheres

TL;DR

This paper proves that certain embedded minimal or constant mean curvature annuli with specific tangency conditions are necessarily rotational, extending understanding of their geometric symmetry.

Contribution

It establishes that such annuli with non-vanishing Gaussian curvature are rotational, under tangency conditions to spheres and planes, revealing new symmetry properties.

Findings

Annuli are rotational under given conditions

Non-vanishing Gaussian curvature is crucial

Tangent conditions determine symmetry

Abstract

We show that a compact embedded minimal or constant mean curvature annulus with non-vanishing Gaussian curvature which is tangent to two spheres of same radius or tangent to a sphere and meeting a plane in constant contact angle is rotational.