Free boundary minimal annuli in geodesic balls of $\mathbb{H}^3$

TL;DR

This paper constructs multiple families of non-rotational minimal annuli with free boundary in hyperbolic 3-space, revealing bifurcations from hyperbolic catenoids and emphasizing symmetry properties.

Contribution

It introduces new non-rotational minimal annuli in hyperbolic space, expanding understanding of free boundary minimal surfaces and their bifurcation phenomena.

Findings

Countable families of minimal annuli constructed

Surfaces share common prismatic symmetry groups

Bifurcation from hyperbolic catenoids observed

Abstract

We construct a countable collection of one-parameter families of non-rotational minimal annuli with free boundary in geodesic balls of hyperbolic 3-space. Every surface within a given family shares a common prismatic symmetry group, and they appear as bifurcations from certain free boundary hyperbolic catenoids.