On the Gauss map of complete spacelike hypersurfaces with bounded mean curvature in the Minkowski space
type: Item
instance of: scholarly article
title: On the Gauss map of complete spacelike hypersurfaces with bounded mean curvature in the Minkowski space
zbMATH Open document ID: 1235.53024
author: Henrique Fernandes de Lima
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 2011-10-27T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bbms/1313604456
review text: The paper deals with a complete space-like hypersurface \(\Sigma^{n}\subset \mathbb{L}^{n+1}\) bounded away from the past infinite of the Minkowski space \(\mathbb{L}^{n+1}\) with bounded mean curvature \(H>0\). The author shows that if the hyperbolic image of the \(n\)-dimensional connected manifold \(\Sigma^{n}\) is contained in the closure of a geodesic ball of centre \(e_{n+1}\in\mathbb{H}^{n}\), where \(\mathbb{H}^{n}\) is the \(n\)-dimensional hyperbolic space the radius \(\rho\) of which satisfies \[ \cosh \rho\leq 1 + \inf_{\Sigma}H, \] then \(\Sigma^{n}\) is a space-like hyperplane.
reviewed by: Fortuné Massamba
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 5964516
zbMATH Keywords: Gauss map
zbMATH Keywords: space-like hypersurface
zbMATH Keywords: Minkowski space
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5964516