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arXiv · 1111.0851

Minimal ends in H2xR with finite total curvature and a Schoen type theorem

Laurent Hauswirth·Barbara Nelli·Ricardo Sa Earp·Eric Toubiana
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Abstract

In this paper we prove that a complete minimal surface immersed in H^2xR, with finite total curvature and two ends, each one asymptotic to a vertical geodesic plane, must be a horizontal catenoid. Moreover, we give a geometric description of minimal ends of finite total curvature in H^2xR. We also prove that a minimal complete end E with finite total curvature is properly immersed and that the Gaussian curvature of E is locally bounded in terms of the geodesic distance to its boundary.

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Laurent Hauswirth, Barbara Nelli, Ricardo Sa Earp, Eric Toubiana. 2011-11-03. Minimal ends in H2xR with finite total curvature and a Schoen type theorem. https://arxiv.org/abs/1111.0851

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