# Constant mean curvature surfaces in hyperbolic 3-space via loop groups

@inproceedings{Dorfmeister2011ConstantMC,
title={Constant mean curvature surfaces in hyperbolic 3-space via loop groups},
author={Josef Dorfmeister and Jun-Ichi Inoguchi and Shimpei Kobayashi},
year={2011}
}
In hyperbolic 3-space $\mathbb{H}^3$ surfaces of constant mean curvature $H$ come in three types, corresponding to the cases $0 \leq H 1$. Via the Lawson correspondence the latter two cases correspond to constant mean curvature surfaces in Euclidean 3-space $\mathbb{E}^3$ with H=0 and $H \neq 0$, respectively. These surface classes have been investigated intensively in the literature. For the case $0 \leq H < 1$ there is no Lawson correspondence in Euclidean space and there are relatively few… CONTINUE READING