Minimal annuli with constant contact angle along the planar boundaries

TL;DR

This paper proves that an immersed minimal annulus with planar boundary curves meeting the planes at a constant contact angle must be part of a catenoid, characterizing such surfaces uniquely.

Contribution

It establishes a uniqueness result for minimal annuli with constant contact angle boundary conditions, linking them specifically to catenoids.

Findings

Any immersed minimal annulus with the given boundary conditions is part of a catenoid.

The boundary conditions enforce a specific geometric structure.

The result characterizes minimal annuli with constant contact angles uniquely as catenoids.

Abstract

We show that an immersed minimal annulus, with two planar boundary curves along which the surface meets these planes with constant contact angle, is part of the catenoid.