Variational problems concerning sub-Finsler metrics in Carnot groups

This paper is devoted to the study of geodesic distances defined on a subdomain given Carnot group, which are bounded both from above and below by fixed multiples Carnot–Carathéodory distance. We show that uniform convergence (on compact sets) these can be equivalently characterized in terms Γ-convergence several kinds variational problems. Moreover, we investigate relation between class intrinsic distances, their metric derivatives sub-Finsler convex metrics horizontal bundle.