Area estimates and rigidity of capillary $H-$surfaces in three-manifolds with boundary
Differential Geometry
2016-04-19 v2
Abstract
We obtain a bound for the area of a capillary surface in a three-manifold with umbilic boundary and controlled sectional curvature. We then analyze the geometry when this area bound is realized, and obtain rigidity theorems. As a side product, we obtain existence of totally geodesic embedded surfaces in hyperbolic three-manifolds under the assumption of the existence of a surface realizing the area bound, in particular, under the existence of a totally umbilic surface.
Keywords
Cite
@article{arxiv.1511.03096,
title = {Area estimates and rigidity of capillary $H-$surfaces in three-manifolds with boundary},
author = {José M. Espinar and Harold Rosenberg},
journal= {arXiv preprint arXiv:1511.03096},
year = {2016}
}
Comments
We discovered we needed to add a hypothesis in Theorem 5.1 {that Sigma separates M) and thus the theorem and its proof has been changed