Periodic constant mean curvature surfaces in \(\mathbb{H}^2 \times \mathbb{R}\)
type: Item
instance of: scholarly article
title: Periodic constant mean curvature surfaces in \(\mathbb{H}^2 \times \mathbb{R}\)
zbMATH Open document ID: 1311.53008
author: Laurent Mazet
author: M. Magdalena Rodríguez
author: Harold Rosenberg
published in: The Asian Journal of Mathematics
publication date: 2015-01-23T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ajm/1417489244
review text: The authors consider periodic surfaces in \(\mathbb{H}^2\times \mathbb{R}\), where \(\mathbb{H}^2\) is the hyperbolic plane defined by the Poincaré disk model. Denoting \(\mathbb{M}=\mathbb{H}^2\times \mathbb{R}/G\), where \(G\) is the discrete group of isometries of \(\mathbb{H}^2\times \mathbb{R}\) generated by horizontal translations along geodesics and/or a vertical translation, they prove an Alexandrov-type theorem for double periodic H-surfaces \(\Sigma \subset \mathbb{M}\) (Theorem 3.1). Various examples of periodic minimal surfaces in \(\mathbb{H}^2\times \mathbb{R}\) are presented.
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 6390114
zbMATH Keywords: constant mean curvature surfaces
zbMATH Keywords: minimal surfaces
zbMATH Keywords: periodic surfaces
zbMATH Keywords: Alexandrov problem
zbMATH Keywords: Alexandrov reflection technique
MaRDI profile type: Publication
DOI: 10.4310/AJM.2014.V18.N5.A4
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description: scientific article; zbMATH DE number 6390114