Abstract
Given a positive function F on S n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature M r for hypersurfaces in ℝn+1 which is a generalization of the usual r-th mean curvature H r . We get integral formulas of Minkowski type for compact hypersurfaces in R n+1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F = 1 which reduces to some well-known results.
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The first author is supported partially by Tianyuan Fund for Mathematics of NSFC (Grant No. 10526030)
The second author is supported partially by Grant No. 10531090 of the NSFC and by Doctoral Program Foundation of the Ministry of Education of China (2006)
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He, Y.J., Li, H.Z. Integral formula of Minkowski type and new characterization of the Wulff shape. Acta. Math. Sin.-English Ser. 24, 697–704 (2008). https://doi.org/10.1007/s10114-007-7116-6
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DOI: https://doi.org/10.1007/s10114-007-7116-6
Keywords
- Wulff shape
- F-Weingarten operator
- anisotropic principal curvature
- r-th anisotropic mean curvature
- integral formula of Minkowski type