English

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

Differential Geometry 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0703187,
  title  = {Integral formula of Minkowski type and new characterization of the Wulff shape},
  author = {Yijun He and Haizhong Li},
  journal= {arXiv preprint arXiv:math/0703187},
  year   = {2007}
}

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10 pages