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Given a positive function $F$ on $S^n$ which satisfies a convexity condition,for $1\leq r\leq n$, we define the $r$-th anisotropic mean curvature function$H^F_r$ for hypersurfaces in $\mathbb{R}^{n+1}$ which is a generalization ofthe usual $r$-th mean curvature function. We prove that a compact embeddedhypersurface without boundary in $\R^{n+1}$ with $H^F_r={constant}$ is theWulff shape, up to translations and homotheties. In case $r=1$, our result isthe anisotropic version of Alexandrov Theorem, which gives an affirmativeanswer to an open problem of F. Morgan.

Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures