Tohoku Mathematical Journal

On stable constant mean curvature hypersurfaces

Hai-Ping Fu and Zhen-Qi Li

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We study complete non-compact stable constant mean curvature hypersurfaces in a Riemannian manifold of bounded geometry, and prove that there are no nontrivial $L^2$ harmonic 1-forms on such hypersurfaces. We also show that any smooth map with finite energy from such a hypersurface to a compact manifold with non-positive sectional curvature is homotopic to constant on each compact set. In particular, we obtain some one-end theorems of complete non-compact weakly stable constant mean curvature hypersurfaces in the space forms.

Article information

Tohoku Math. J. (2), Volume 62, Number 3 (2010), 383-392.

First available in Project Euclid: 15 October 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 58E20: Harmonic maps [See also 53C43], etc.

Stable hypersurface $L^2$ harmonic forms constant mean curvature harmonic map ends


Fu, Hai-Ping; Li, Zhen-Qi. On stable constant mean curvature hypersurfaces. Tohoku Math. J. (2) 62 (2010), no. 3, 383--392. doi:10.2748/tmj/1287148618.

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