Properly embedded, area-minimizing surfaces in hyperbolic $3$-space
Differential Geometry
2014-01-14 v3
Abstract
We prove prove a bridge principle at infinity for area-minimizing surfaces in the hyperbolic space , and we use it to prove that any open, connected, orientable surface can be properly embedded in as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that the limit sets of different ends are disjoint.
Cite
@article{arxiv.1302.5159,
title = {Properly embedded, area-minimizing surfaces in hyperbolic $3$-space},
author = {Francisco Martin and Brian White},
journal= {arXiv preprint arXiv:1302.5159},
year = {2014}
}
Comments
25 pages, 3 figures. This revised version will appear in Journal of Differential Geometry