Calculus of Variations and Geometric Measure Theory

V. Magnani

On a general coarea inequality and applications

created on 04 Nov 2000
modified on 24 Apr 2004


Published Paper

Inserted: 4 nov 2000
Last Updated: 24 apr 2004

Journal: Ann. Acad. Sci. Fenn. Math.
Volume: 27
Pages: 121-140
Year: 2002


We prove a coarea inequality for Lipschitz maps between stratified groups. As a consequence we obtain a Sard-type theorem and the nonexistence of nontrivial coarea formulae between Heisenberg groups. In the case of real valued Lipschitz maps on the Heisenberg group we get a coarea formula using the $Q-1$ spherical Hausdorff measure restricted to level sets, where $Q$ is the homogeneous dimension of the group.

Keywords: stratified groups, coarea formula, perimeter measure