Compact spacelike surfaces with constant mean curvature in the Lorentz-Minkowski 3-space
type: Item
instance of: scholarly article
title: Compact spacelike surfaces with constant mean curvature in the Lorentz-Minkowski 3-space
zbMATH Open document ID: 0934.53040
author: Rafael López
author: José A. Pastor
author: Luis J. Alías
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2000-04-10T00:00:00Z
review text: The authors prove some integral formulas for compact spacelike surfaces with constant mean curvature in the Lorentz-Minkowski three-space \(L^3\). They give some uniqueness results. For instance, ``The only immersed compact spacelike surfaces with constant mean curvature in \(L^3\) spanning a circle are the planar discs and the hyperbolic caps'', and also: ``Let \(\Sigma_1\) and \(\Sigma_2\) be two compact spacelike constant mean curvature surfaces bounded by a curve which projects onto a planar Jordan curve contained inspacelike plane. If they have the same mean curvature, then \(\Sigma_1= \Sigma_2\)''.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1275221
zbMATH Keywords: integral formulas
zbMATH Keywords: constant mean curvature
zbMATH Keywords: spacelike surfaces
reviewed by: Bernard Rouxel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178224893
OpenAlex ID: W2088952777
cites work: The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space
cites work: A characteristic property of spheres
cites work: Spacelike hypersurfaces with prescribed boundary values and mean curvature
cites work: Q3974685
cites work: Q5187597
cites work: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary
cites work: Compact constant mean curvature surfaces in Euclidean three-space
cites work: Symmetry of hypersurfaces of constant mean curvature with symmetric boundary
cites work: The structure of complete embedded surfaces with constant mean curvature
cites work: Constant Mean Curvature Discs with Bounded Area
cites work: Constant mean curvature surfaces with planar boundary
cites work: Constant mean curvature surfaces in a half-space of \(\mathbb{R}^ 3\) with boundary in the boundary of the half-space
cites work: Entire spacelike hypersurfaces of constant mean curvature in Minkowski space
cites work: Constant mean curvature surface, harmonic maps, and universal Teichmüller space
DOI: 10.2748/TMJ/1178224893
description: scientific article; zbMATH DE number 1275221