On the stability of the Wulff shape

Abstract

Given a positive function F on S n satisfying an appropriate convexity assumption, we consider hypersurfaces for which a linear combination of some higher order anisotropic curvatures is constant. We define the variational 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.