On embedded minimal surfaces of Costa-Hoffman-Meeks type in hyperbolic space

TL;DR

This paper introduces a novel construction of embedded minimal surfaces in hyperbolic space that have three asymptotically totally geodesic ends and arbitrary finite genus, expanding the understanding of minimal surface configurations.

Contribution

It provides a new method for constructing embedded minimal surfaces with specific geometric properties in hyperbolic space, including multiple ends and arbitrary genus.

Findings

Constructed new examples of minimal surfaces with three ends

Surfaces have arbitrary finite genus

Method applicable to hyperbolic space

Abstract

We present a new construction of embedded minimal surfaces in hyperbolic space with $3$ asymptotically totally geodesic ends and arbitrary finite genus.