Some structure theorems for complete \(H\)-surfaces in hyperbolic 3-space \(\mathbb{H}^3\)
type: Item
instance of: scholarly article
title: Some structure theorems for complete \(H\)-surfaces in hyperbolic 3-space \(\mathbb{H}^3\)
zbMATH Open document ID: 0904.53042
author: Beate Semmler
published in: Illinois Journal of Mathematics
publication date: 1999-01-11T00:00:00Z
review text: We consider properly embedded complete noncompact (nonzero) constant mean curvature surfaces \(M\) of finite topology in hyperbolic 3-space with boundary a strictly convex curve \(C\) in a geodesic plane \(P\). Assume \(M\) is transverse to \(P\) along \(C\) and has a finite number of cylindrically bounded ends orthogonal to \(P\) contained in one of the half-spaces determined by \(P\). We prove that if \(M\) is contained in the half-space, then \(M\) inherits the symmetries of \(C\). In particular, \(M\) is a Delaunay surface if \(C\) is a circle. Then we give conditions that ensure that if \(M\) is contained in the half-space only near \(C\), \(M\) is entirely in the half-space.
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 1191159
zbMATH Keywords: noncompact surfaces of constant mean curvature with boundary
zbMATH Keywords: Alexandrov reflection principle
zbMATH Keywords: flux formula
zbMATH Keywords: Delaunay surfaces
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1191159