Intrinsic regular hypersurfaces in Heisenberg groups

We study the H-regular surfaces, a class of intrinsic regular hypersurfaces in the setting of the Heisenberg group H^n = C^n x R = R^{2n+1} endowed with a left-invariant metric d equivalent to its Carnot-Carathéodory (CC) metric. Here hypersurface simply means topological codimension 1 surface and by the words "'intrinsic'" and "'regular" we mean, respectively, notions involving the group structure of H^n and its differential structure as CC manifold. In particular, we characterize these surfaces as intrinsic regular graphs inside H^n by studying the intrinsic regularity of the parameterizations and giving an area-type formula for their intrinsic surface measure.