Intrinsically Lipschitz functions with normal target in Carnot groups

Abstract

We provide a Rademacher theorem for intrinsically Lipschitz functions \(\phi\colon U\subseteq\mathbf{W}\to\mathbf{L}\), where \(U\) is a Borel set, \(\mathbf{W}\) and \(\mathbf{L}\) are complementary subgroups of a Carnot group, where we require that \(\mathbf{L}\) is a normal subgroup. Our hypotheses are satisfied for example when \(\mathbf{W}\) is a horizontal subgroup. Moreover, we provide an area formula for this class of intrinsically Lipschitz functions.