A characterization of spheres in Euclidean space
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.
scientific article; zbMATH DE number 4075953