Anisotropic motion by mean curvature in the context of Finsler geometry

Abstract. We study the anisotropic motion of a hypersurface in the context of the geometry of Finsler spaces. This amounts in considering the evolution in relative geometry, where all quantities are referred to the given Finsler metric \phi representing the anisotropy, which we allow to be a function of space. Assuming that \phi is strictly convex and smooth, we prove that the natural evolution law is of the form “velocity =H_{\phi}”, where