Stability of compact constant mean curvature hypersurfaces in a wide class of Riemannian manifolds (Q438942)
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scientific article; zbMATH DE number 6062599
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of compact constant mean curvature hypersurfaces in a wide class of Riemannian manifolds |
scientific article; zbMATH DE number 6062599 |
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Stability of compact constant mean curvature hypersurfaces in a wide class of Riemannian manifolds (English)
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31 July 2012
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The authors generalizes to a wide class of Riemannian manifolds, including space forms, the result stating that ``the only stable compact hypersurfaces on constant mean curvature immersed in space forms are geodesic spheres'' [\textit{J. L. Barbosa} and \textit{M. P. do Carmo}, Math. Z. 185, 339--353 (1984; Zbl 0513.53002); \textit{J. L. Barbosa, M. P. do Carmo} and \textit{J.-H. Eschenburg}, Math. Z. 197, No. 1, 123--138 (1988; Zbl 0653.53045)]. The interest of this work lies mostly on the simplicity of the proof.
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immersion
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stable
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hypersurface
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constant mean curvature
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Einstein
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