×

zbMATH — the first resource for mathematics

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
MSC:
53C40 Global submanifolds
53A05 Surfaces in Euclidean and related spaces
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
PDF BibTeX XML Cite
Full Text: EuDML