Periodic constant mean curvature surfaces in H^2 x R
Differential Geometry
2011-06-30 v1
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.
Keywords
Cite
@article{arxiv.1106.5900,
title = {Periodic constant mean curvature surfaces in H^2 x R},
author = {Laurent Mazet and M. Magdalena Rodríguez and Harold Rosenberg},
journal= {arXiv preprint arXiv:1106.5900},
year = {2011}
}