Regular submanifolds, graphs and area formula in Heisenberg groups (Q876324)

The paper describes intrinsically regular submanifolds in Heisenburg groups \({\mathbb H}^n\). 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 the authors prove that they are graphs in a natural group way, as well as that an area formula holds for the intrinsic Hausdorff measure. Finally, they can be seen as Federer-Fleming currents given a natural complex of differential form on \({\mathbb H}^n\).