Intrinsic regular hypersurfaces in Heisenberg groups

We study the H-regular surfaces, a class of intrinsic regular hypersurfaces in the selling of the Heisenberg group H-n = C-n x R = R2n+1 endowed with a left-invariant metric d(infinity) equivalent to its Carnot-Caratheodory (CC) metric. Here hypersurface simply means topological codimension 1 surface and by the words "intrinsic" and "regular" we mean, respectively nations 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.