The influence of the boundary behaviour on hypersurfaces with constant mean curvature in \(H^{n+1}\)
type: Item
instance of: scholarly article
title: The influence of the boundary behaviour on hypersurfaces with constant mean curvature in \(H^{n+1}\)
zbMATH Open document ID: 0614.53046
DOI: 10.1007/BF02621926
published in: Commentarii Mathematici Helvetici
publication date: 1986-01-01T00:00:00Z
review text: The asymptotic boundary of complete H-hypersurfaces in the hyperbolic space is studied. There are results of the following type: If \(H\in [0,1)\) then there is an a priori lower bound for the distance between components of the asymptotic boundary, which is attained only for rotational hypersurfaces of spherical type. For \(H\neq 1\) the latter are also characterized by the fact that its boundary consists of two disjoint (n-1)-spheres, and M is regular at infinity.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 3994474
zbMATH Keywords: constant mean curvature
zbMATH Keywords: boundary regularity
zbMATH Keywords: Alexandrov maximum principle
zbMATH Keywords: asymptotic boundary
zbMATH Keywords: rotational hypersurfaces
author: Manfredo P. do Carmo
author: Jonas de Miranda Gomes
author: Gudlaugur Thorbergsson
reviewed by: Dirk Ferus
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf02621926
OpenAlex ID: W1971918417
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description: scientific article; zbMATH DE number 3994474