Closed Minimal Surfaces in Cusped Hyperbolic Three-manifolds
Differential Geometry
2016-12-20 v3 Geometric Topology
Abstract
Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of finite volume. We prove any closed immersed incompressible surface can be deformed to a closed immersed least area surface within its homotopy class in any cusped hyperbolic three-manifold. Our techniques highlight how special structures of these cusped hyperbolic three-manifolds prevent any least area minimal surface going too deep into the cusped region.
Cite
@article{arxiv.1507.04818,
title = {Closed Minimal Surfaces in Cusped Hyperbolic Three-manifolds},
author = {Zheng Huang and Biao Wang},
journal= {arXiv preprint arXiv:1507.04818},
year = {2016}
}
Comments
23 pages, 2 figures: Final version, to appear in Geometriae Dedicata