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

2011/11/03 by Hauswirth, Laurent, Nelli, Barbara, Earp, Ricardo Sa +1
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.0851

Abstract

In this paper we prove that a complete minimal surface immersed in H²xR, 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 H²xR. 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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