# Minimal n-Noids in Hyperbolic and Anti-de Sitter 3-Space

Alexander I. Bobenko, Sebastian Heller, Nicholas Schmitt

### Description

We show 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 $\mathrm{S}^3=\mathrm{H}^3\cup\mathrm{S}^2\cup\mathrm{H}^3$. [1]

### References

• Alexander I Bobenko, Sebastian Heller, and Nicholas Schmitt.
Minimal n-Noids in hyperbolic and anti-de Sitter 3-space.
Proceedings A of Royal Society, July 2019.
arXiv:1902.07992, doi:10.1098/rspa.2019.0173.

#### Prof. Dr. Alexander I. Bobenko   +

Projects: A01, A02, C01, B02, Z, CaP, II
University: TU Berlin, Institut für Mathematik, MA 881