Let k be a positive integer and let m be the dimension of the horizontal subspace of a stratified group. Under the condition that k is not greater than m, we show that all submanifolds of codimension k are generically non-horizontal. For these submanifolds, we prove an area-type formula that allows us to compute their Q - k dimensional spherical Hausdorff measure. Finally, we observe that almost every level set of a sufficiently regular vector-valued mapping on a stratified group is a non-horizontal submanifold. This allows us to establish a sub-Riemannian coarea formula for vector-valued Riemannian Lipschitz mappings on stratified groups.
Autori interni: | ||
Autori: | VALENTINO MAGNANI | |
Titolo: | Non-horizontal submanifolds and coarea formula | |
Anno del prodotto: | 2008 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |