# Minimal n-Noids in hyperbolic and anti-de Sitter 3-space

## TL;DR

This paper constructs minimal surfaces with n-punctured sphere topology in hyperbolic and anti-de Sitter 3-space using loop group methods, analyzing their asymptotics and extensions to Willmore surfaces.

## Contribution

It introduces a novel construction of minimal n-noids in hyperbolic and anti-de Sitter spaces via loop group factorization, expanding the understanding of their asymptotic behavior.

## Key findings

- Constructed minimal n-noids in hyperbolic and anti-de Sitter 3-space.
- Analyzed asymptotics based on Delaunay-type surfaces.
- Extended minimal surfaces to Willmore surfaces in conformal 3-sphere.

## Abstract

We construct minimal surfaces in hyperbolic and anti-de Sitter 3-space with the topology of a $n$-punctured sphere by loop group factorization methods. The end behavior of the surfaces is based on the asymptotics of Delaunay-type surfaces, i.e., rotational symmetric minimal cylinders. The minimal surfaces in $\mathrm{H}^3$ extend to Willmore surfaces in the conformal 3-sphere $\mathrm{S}^3=\mathrm{H}^3\cup\mathrm{S}^2\cup\mathrm{H}^3$.