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2008 The structure of weakly stable constant mean curvature hypersurfaces
Xu Cheng, Leung-fu Cheung, Detang Zhou
Tohoku Math. J. (2) 60(1): 101-121 (2008). DOI: 10.2748/tmj/1206734408

Abstract

We study the global behavior of weakly stable constant mean curvature hypersurfaces in a Riemannian manifold by using harmonic function theory. In particular, a complete oriented weakly stable minimal hypersurface in the Euclidean space must have only one end. Any complete noncompact weakly stable hypersurface with constant mean curvature $H$ in the 4 and 5 dimensional hyperbolic spaces has only one end under some restrictions on $H$.

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Xu Cheng. Leung-fu Cheung. Detang Zhou. "The structure of weakly stable constant mean curvature hypersurfaces." Tohoku Math. J. (2) 60 (1) 101 - 121, 2008. https://doi.org/10.2748/tmj/1206734408

Information

Published: 2008
First available in Project Euclid: 28 March 2008

zbMATH: 1154.53036
MathSciNet: MR2419038
Digital Object Identifier: 10.2748/tmj/1206734408

Subjects:
Primary: 53C42
Secondary: 53C21

Rights: Copyright © 2008 Tohoku University

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