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Article Dans Une Revue Asian Journal of Mathematics Année : 2014

Periodic constant mean curvature surfaces in $\mathbb H^2\times \mathbb R$

Résumé

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.

Dates et versions

hal-00627434 , version 1 (28-09-2011)

Identifiants

Citer

Laurent Mazet, M. Magdalena Rodriguez, Harold Rosenberg. Periodic constant mean curvature surfaces in $\mathbb H^2\times \mathbb R$. Asian Journal of Mathematics, 2014, pp.829--858. ⟨10.4310/AJM.2014.v18.n5.a4⟩. ⟨hal-00627434⟩
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