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arXiv · 1106.5900

Periodic constant mean curvature surfaces in H^2 x R

Laurent Mazet·M. Magdalena Rodríguez·Harold Rosenberg
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Abstract

In this paper we study minimal and constant mean curvature (cmc) periodic surfaces in H^2 x R. More precisely, we consider quotients of H^2 x R by discrete groups of isometries generated by horizontal hyperbolic translations f and/or a vertical translation T. In the quotient by the Z^2 subgroup of the isometry group generated by any f and T, we prove an Alexandrov-type theorem for cmc surfaces, i.e., an analysis of compact embedded cmc surfaces in such a quotient. The remainder of the paper is devoted to construct examples of periodic minimal surfaces in H^2 x R.

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Laurent Mazet, M. Magdalena Rodríguez, Harold Rosenberg. 2011-06-29. Periodic constant mean curvature surfaces in H^2 x R. https://arxiv.org/abs/1106.5900

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