Regular submanifolds, graphs and area formula in Heisenberg groups

We describe intrinsically regular submanifolds in Heisenberg groups $he n$. Low dimensional and low codimensional submanifolds turn out to be of a very different nature. The first ones are Legendrian surfaces, while low codimensional ones are more general objects, possibly non Euclidean rectifiable. Nevertheless we prove that they are graphs in a natural group way, as well as that an area formula holds for the intrinsic Haudorff measure. Finally, they can be seen as Federer-Fleming currents given a natural complex of differential forms on the Heisenberg group.