Some integral formulas for hypersurfaces and a generalization of the Hilbert-Liebmann theorem
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- Proc. Amer. Math. Soc. 88 (1983), 326-329 Request permission
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.References
- Robert C. Reilly, Variational properties of functions of the mean curvatures for hypersurfaces in space forms, J. Differential Geometry 8 (1973), 465–477. MR 341351
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
Additional Information
- © Copyright 1983 American Mathematical Society
- 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