Lipschitz graphs and currents in Heisenberg groups

Abstract The main result of the present article is a Rademacher-type theorem for intrinsic Lipschitz graphs codimension $k\leq n$ in sub-Riemannian Heisenberg groups ${\mathbb H}^{n}$ . For purpose proving such result, we settle several related questions pertaining both to theory and one currents. First, prove an extension as well uniform approximation by means smooth graphs: these results stem from new definition (equivalent introduced B. Franchi, R. Serapioni F. Serra Cassano) are valid more general class Carnot groups. Second, our proof Rademacher’s heavily uses language currents groups: key is, us, version celebrated constancy theorem. Inasmuch defined terms Rumin’s complex differential forms, also provide convenient basis spaces. Eventually, some applications including Lusin-type graphs, equivalence between H}$ -rectifiability ‘Lipschitz’ area formula