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

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 ${\mathrm{S}}^3={\mathrm{H}}^3\cup {\mathrm{S}}^2\cup {\mathrm{H}}^3$.

26 pages, 7 figures