Generalized Mean Curvature Flow in Carnot Groups

In this paper we study the generalized mean curvature flow of sets in the sub-Riemannian geometry of Carnot groups. We extend to our context the level sets method and the weak (viscosity) solutions introduced in the Euclidean setting in [4] and [12]. We establish two special cases of the comparison principle, existence, uniqueness and basic geometric properties of the flow