Calculus of Variations and Geometric Measure Theory

V. Magnani

Note on coarea formulae in the Heisenberg group

created by magnani on 11 Jan 2012


Published Paper

Inserted: 11 jan 2012
Last Updated: 11 jan 2012

Journal: Publ. Mat.
Volume: 48
Number: 2
Pages: 409-422
Year: 2004


We show a fi rst nontrivial example of coarea formula for vector-valued Lipschitz maps defi ned on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed with respect to the 2-dimensional spherical Hausdor ff measure, built by the Carnot-Carathéodory distance. The standard Jacobian is replaced by the so called "horizontal jacobian", corresponding to the Jacobian of the Pansu differential of the Lipschitz map. Joining previous results, we achieve all possible coarea formulae for Lipschitz maps de ned on the Heisenberg group.

Keywords: coarea formulae, Heisenberg group