Calculus of Variations and Geometric Measure Theory

B. Franchi - R. Serapioni - F. Serra Cassano

Regular submanifolds, graphs and area formula in Heisenberg groups

created by serapion on 15 Jun 2005
modified by serracas on 18 Dec 2006


Accepted Paper

Inserted: 15 jun 2005
Last Updated: 18 dec 2006

Journal: Advances in Mathematics
Year: 2004


We describe intrinsically regular submanifolds in Heisenberg groups $H^n$. 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 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 $H^n$.

Keywords: area formula, Heisenberg groups, regular submanifolds, Federer-Fleming currents