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An integral formula for closed surfaces and a generalization of Hp- theorem. (English) Zbl 0651.53042
Let F be a closed, immersed, and orientable \(C^{\infty}\) surface in \({\mathbb{R}}^ 3\). The author shows that if \(Hp=1\) on F, where H is the mean curvature, and p is the support function, then F is a standard sphere. Previously this result has been proved under the additional assumption that the Gauss curvature of F is positive.
Reviewer: V.Oliker
53C40 Global submanifolds
53A05 Surfaces in Euclidean and related spaces
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
Full Text: EuDML