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Proceedings of the American Mathematical Society

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Some integral formulas for hypersurfaces and a generalization of the Hilbert-Liebmann theorem


Author: An Min Li
Journal: Proc. Amer. Math. Soc. 88 (1983), 326-329
MSC: Primary 53C40
DOI: https://doi.org/10.1090/S0002-9939-1983-0695268-0
MathSciNet review: 695268
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Abstract: R. C. Reilly calculated the variations of functions of the mean curvatures for hypersurfaces in Euclidean space. In the present paper, using Reilly's formulas, we derive some general integral formulas for hypersurfaces, which generalize the well-known Minkowski formulas, and then apply those formulas to obtain some characterizations of the hypersphere.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0695268-0
Article copyright: © Copyright 1983 American Mathematical Society