Minimal surfaces in finite volume non compact hyperbolic $3$-manifolds
Differential Geometry
2014-06-26 v2
Abstract
We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic -manifold . We also obtain a least area, incompressible, properly embedded, finite topology, -sided surface. We prove a properly embedded minimal surface of bounded curvature has finite topology. This determines its asymptotic behavior. Some rigidity theorems are obtained.
Keywords
Cite
@article{arxiv.1405.1324,
title = {Minimal surfaces in finite volume non compact hyperbolic $3$-manifolds},
author = {Pascal Collin and Laurent Hauswirth and Laurent Mazet and Harold Rosenberg},
journal= {arXiv preprint arXiv:1405.1324},
year = {2014}
}