A characterization of spheres in Euclidean space (Q1111161)
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scientific article; zbMATH DE number 4075953
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of spheres in Euclidean space |
scientific article; zbMATH DE number 4075953 |
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A characterization of spheres in Euclidean space (English)
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1988
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It is proven that a complete properly embedded surface with constant mean curvature, contained in a plane cone of \(E^ 3\), must be a round sphere. This generalizes a well-known theorem due \textit{A. D. Alexandrov} [Ann. Math. Pure Appl., IV. Ser. 58, 303-315 (1962; Zbl 0107.156)] on the characterization of spheres.
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embedded surface
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constant mean curvature
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