Existence and uniqueness for anisotropic and crystalline mean curvature flows
An existence and uniqueness result, up to fattening, for crystalline mean curvature flows with forcing and arbitrary (convex) mobilities is proven. This is achieved by introducing a new notion of solution to the corresponding level set formulation. Such a solution satisfies the comparison principle and a stability property with respect to the approximation by suitably regularized problems. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets.