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

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

2007-03-07

arxiv.org/abs/math/0703187v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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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