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.
On a general coarea inequality and applications
MAGNANI, VALENTINO
2002-01-01
Abstract
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.File in questo prodotto:
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