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arXiv · 1511.03096

Area estimates and rigidity of capillary $H-$surfaces in three-manifolds with boundary

José M. Espinar·Harold Rosenberg
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Abstract

We obtain a bound for the area of a capillary $H-$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 $H-$surface realizing the area bound, in particular, under the existence of a totally umbilic $H-$surface.

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José M. Espinar, Harold Rosenberg. 2015-11-10. Area estimates and rigidity of capillary $H-$surfaces in three-manifolds with boundary. https://arxiv.org/abs/1511.03096

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