A characterization of the delaunay surfaces

Abstract

In this paper we use the Alexandrov Reflection Method to obtain a characterization to embedded CMC capillary annulus ${\Sigma }^2\subset {\mathbb{B}}^3$. In especial, but using a new strategy, we present a new characterization to the critical catenoid. Precisely, we show that $\Sigma \subset {\mathbb{B}}^3$ being an embedded minimal free boundary annulus in ${\mathbb{B}}^3$ such that $\partial \Sigma$ is invariant under reflection through a coordinates planes, then $\Sigma$ is the critical catenoid. This work is part of the second author thesis which was written in 2019.

11 pages, 9 figures