Some characterizations of the Wulff shape [Sur certaines caractérisations des formes de Wulff]

摘要

For a positive function F on S~n which satisfies a suitable convexity condition, we consider the r-th anisotropic mean curvature for hypersurfaces in R~(n+1) which is a generalization of the usual r-th mean curvature H_r. By using an integral formula of Minkowski type for compact hypersurface due to H.J. He and H. Li, we introduce some new characterizations of the Wulff shape.