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 × ℝ = ℝ2n+1 endowed with a leftinvariant metric d∞ 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 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 areatype formula for their intrinsic surface measure.