English

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 H3\mathbb{H}^3, and we use it to prove that any open, connected, orientable surface can be properly embedded in H3\mathbb{H}^3 as an area-minimizing surface. Moreover, the embedding can be constructed in such a way that the limit sets of different ends are disjoint.

Keywords

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

R2 v1 2026-06-21T23:29:49.782Z