A $\sigma$-homothetic uniqueness of the critical catenoid

TL;DR

This paper proves a uniqueness result for free boundary minimal annuli in the unit ball that are related to the critical catenoid through a specific scaling transformation.

Contribution

It establishes the $\sigma$-homothetic uniqueness of the critical catenoid among free boundary minimal annuli.

Findings

Uniqueness of the critical catenoid under $\sigma$-homothety.

Characterization of free boundary minimal annuli in the unit ball.

Extension of classical minimal surface uniqueness results.

Abstract

We prove a uniqueness result for free boundary minimal annuli in the unit Euclidean three-ball that are $\sigma$-homothetic to the critical catenoid.