  Given a positive function F on S n satisfying an appropriate con-vexity
assumption, we consider hypersurfaces for which a linear combination of some
higher order anisotropic curvatures is constant. We define the varia-tional
problem for which these hypersurfaces are critical points and we prove that, up
to translations and homotheties, the Wulff shape is the only stable closed
hypersurface of the Euclidean space for this problem.
