Tohoku Mathematical Journal

The structure of weakly stable constant mean curvature hypersurfaces

Xu Cheng, Leung-fu Cheung, and Detang Zhou

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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 $H$.

Article information

Tohoku Math. J. (2), Volume 60, Number 1 (2008), 101-121.

First available in Project Euclid: 28 March 2008

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Zentralblatt MATH identifier

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

hypersurfaces constant mean curvature harmonic function


Cheng, Xu; Cheung, Leung-fu; Zhou, Detang. The structure of weakly stable constant mean curvature hypersurfaces. Tohoku Math. J. (2) 60 (2008), no. 1, 101--121. doi:10.2748/tmj/1206734408.

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