Area monotonicity for spacelike surfaces with constant mean curvature
type: Item
instance of: scholarly article
title: Area monotonicity for spacelike surfaces with constant mean curvature
zbMATH Open document ID: 1074.53051
author: Rafael López
published in: Journal of Geometry and Physics
publication date: 2005-06-13T00:00:00Z
review text: Compact space-like surfaces \(\Sigma\) with constant mean curvature \(H\) in the three-dimensional Lorentz-Minkowski space \(\mathbb{L}^3\) are considered, assuming that the boundary is a plane curve. An estimate is obtained for the height \(h\) of the surface measured from the plane \(\Pi\) that contains the boundary. It is established that \(h\leq A|H|/(2\pi)\), where \(A\) is the area of the surface that lies over \(\Pi\). Equality holds if and only if \(\Sigma\) is a planar domain \((H= 0)\) or a hyperbolic cap \((H\neq 0)\) (i.e., a compact piece of a hyperbolic plane with the circular boundary.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 2175260
zbMATH Keywords: space-like surface
zbMATH Keywords: constant mean curvature
zbMATH Keywords: co-area formula
reviewed by: Ülo Lumiste
MaRDI profile type: Publication
full work available at URL: j.geomphys.2004.03.008
OpenAlex ID: W2074181090
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DOI: 10.1016/J.GEOMPHYS.2004.03.008
description: scientific article; zbMATH DE number 2175260