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

By Yijun He, Haizhong Li. 2007

61 citations recorded by the source corpus.

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 the use of our integral formulas of Minkowski type, in case F = 1 which reduces to some well-known results.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/7d31e34eaa5afad69d7608b47ce8154ea5bc8342

How researchers see this paper

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In Applied Mathematics

1. Haizhong Li
2. Yijun He
3. Jianquan Ge
4. Ben Andrews

In Computational Mechanics

1. Haizhong Li
2. Yijun He

Citations in the corpus

• COMPACT EMBEDDED HYPERSURFACES WITH CONSTANT HIGHER ORDER ANISOTROPIC MEAN CURVATURES (2007, background): “([8], [9]) Let X : M → Rn+1 be an n-dimensional compact hypersurface without boundary, F : Sn → R+ be a smooth function which satisfies (1.”