Anisotropic curvature-driven flow of convex sets

We study in this paper the mean curvature evolution, and in particular the anisotropic mean curvature evolution, of convex sets in RNRN (without driving forces). If the anisotropy is smooth, we show that the evolution remains convex. If the anisotropy is crystalline, we build a convex evolution which satisfies an equation which is a weak form of the crystalline curvature motion equation.