Existence of constant mean curvature graphs in hyperbolic space
type: Item
instance of: scholarly article
title: Existence of constant mean curvature graphs in hyperbolic space
zbMATH Open document ID: 0945.53008
author: Rafael López
author: Sebastián Montiel
published in: Calculus of Variations and Partial Differential Equations
publication date: 2000-09-20T00:00:00Z
review text: In this paper, the authors study graphs of constant mean curvature over a horosphere in hyperbolic space \(H^{n+1}\). The main result is: let \(\Omega \) be a compact domain of a horosphere in \(H^{n+1},\) whose boundary \(\partial \Omega \) is ``mean convex'', that is, its mean curvature \(H_{\partial \Omega }\) is positive with respect to the inner orientation. If \(H\) is a number such that \(-H_{\partial \Omega }<H<1,\) then there exists a graph over \(\Omega \) with constant mean curvature \(H\) and boundary \(\partial \Omega .\)
reviewed by: Jitan Lu
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 1294470
zbMATH Keywords: constant mean curvature graph
zbMATH Keywords: hyperbolic space
zbMATH Keywords: Hopf maximum principle
MaRDI profile type: Publication
full work available at URL: s005260050122
OpenAlex ID: W2395306798
DOI: 10.1007/S005260050122
description: scientific article; zbMATH DE number 1294470