Inserted: 4 nov 2000
Last Updated: 24 apr 2004
Journal: Ann. Acad. Sci. Fenn. Math.
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