Lipschitz Carnot-Carathéodory Structures and their Limits

Abstract In this paper we discuss the convergence of distances associated to converging structures Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under mild controllability assumption limit vector-fields structure, equi-Lipschitz that converge uniformly compact subsets, locally Carnot-Carathéodory distance. case in which distance is boundedly compact, show uniform sets. an example not several examples our result can be applied. Among them, subFinsler Mitchell’s Theorem with norms, general for subspaces Lie algebra connected group.