Stable complete noncompact hypersurfaces with constant mean curvature
type: Item
instance of: scholarly article
title: Stable complete noncompact hypersurfaces with constant mean curvature
zbMATH Open document ID: 1181.53050
author: Jui-Tang Ray Chen
published in: Annals of Global Analysis and Geometry
publication date: 2009-09-09T00:00:00Z
review text: This paper concerns the structure of complete noncompact stable hypersurfaces \(M^{n}\) with constant mean curvature \(H > 0\) in a complete noncompact oriented Riemannian manifold \(N^{n+1}\). In particular, the author shows that a complete noncompact stable constant mean curvature hypersurface \(M^{n },\;n = 5, 6\), in the Euclidean space must have only one end. Any such hypersurface in the hyperbolic space with \(H^{2} > \frac{65}{63},\frac{175}{148},\frac{41}{25},\frac{671}{171}\), for \(n=3,4,5,6\), respectively, has only one end.
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 5602560
zbMATH Keywords: stable hypersurface
zbMATH Keywords: constant mean curvature
zbMATH Keywords: hyperbolic space
zbMATH Keywords: (non)-parabolic end
reviewed by: Vladimir Yu. Rovenskij
MaRDI profile type: Publication
full work available at URL: s10455-009-9155-y
OpenAlex ID: W1973402996
cites work: Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem
cites work: Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
cites work: Minimal cones and the Bernstein problem
cites work: L 2 harmonic forms and stability of hypersurfaces with constant mean curvature
cites work: On constant mean curvature hypersurfaces with finite index
cites work: The structure of weakly stable minimal hypersurfaces
cites work: Stable complete minimal surfaces in 𝑅³ are planes
cites work: The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
cites work: On the oriented Plateau problem
cites work: The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
cites work: \(L^2\) harmonic forms on a complete stable hypersurfaces with constant mean curvature
cites work: Harmonic functions and the structure of complete manifolds
cites work: Complete manifolds with positive spectrum
cites work: Complete manifolds with positive spectrum. II.
cites work: A note on harmonic maps
cites work: Weighted Poincaré inequality and rigidity of complete manifolds
cites work: Connectedness at infinity of complete Kähler manifolds
cites work: Stable Complete Constant Mean Curvature Surfaces in R 3 and H 3
cites work: Minimal varieties in Riemannian manifolds
cites work: Stability of complete noncompact surfaces with constant mean curvature
DOI: 10.1007/S10455-009-9155-Y
description: scientific article; zbMATH DE number 5602560