arXiv math/07031872007-03-07math.DG

Integral formula of Minkowski type and new characterization of the Wulff shape

Yijun He, Haizhong Li

备注：: 10 pages

英文摘要：

Given a positive function F on Sn which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in Rn+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in Rn+1. We give some new characterizations of the Wulff shape by use of our integral formulas of Minkowski type, in case F = 1 which reduces to some well-known results.

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