A Bernstein type theorem in \(\mathbb R\times\mathbb H^n\)
type: Item
instance of: scholarly article
title: A Bernstein type theorem in \(\mathbb R\times\mathbb H^n\)
zbMATH Open document ID: 1276.53067
author: Henrique Fernandes de Lima
author: Ulisses L. Parente
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2013-02-14T00:00:00Z
review text: Using the generalized Omori-Yau maximum principle, the authors prove the following theorem: Let \(\Sigma^n\) be a constant mean curvature, complete immersed hypersurface in \(\mathbb{R}\times \mathbb{H}^n\) such that the second fundamental form \(A\) is bounded. Assume that the angle function is bounded away from zero and that the height function \(h\) satisfies \(|\nabla h|^2\leq {\alpha\over n-1}|A|^2\) with some \(0<\alpha<1\). Then \(\Sigma^n\) is a slice in \(\mathbb{R}\times \mathbb{H}^n\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 6136412
zbMATH Keywords: complete hypersurface
zbMATH Keywords: mean curvature
zbMATH Keywords: vertical graph
reviewed by: Gábor Tóth
MaRDI profile type: Publication
full work available at URL: s00574-012-0003-5
OpenAlex ID: W2045635753
Wikidata QID: Q124851725
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cites work: Isometric immersions of Riemannian manifolds
cites work: Minimal surfaces in \(M^2\times \mathbb{R}\)
DOI: 10.1007/S00574-012-0003-5
description: scientific article; zbMATH DE number 6136412