Stable hypersurfaces with constant mean curvature in \(R^ n\) (Q674585)
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scientific article; zbMATH DE number 986944
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stable hypersurfaces with constant mean curvature in \(R^ n\) |
scientific article; zbMATH DE number 986944 |
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Stable hypersurfaces with constant mean curvature in \(R^ n\) (English)
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23 March 1998
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The author proves that if \(M\) is a complete noncompact stable hypersurface in Euclidean space \(\mathbb{R}^n\) with constant mean curvature and nonnegative Ricci curvature, then \(M\) is a plane. This result partially answers do Carmo's conjecture that a complete noncompact stable hypersurface in \(\mathbb{R}^n\) with constant mean curvature is minimal.
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mean curvature
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Ricci curvature
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stability
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minimal surface
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