Non-horizontal submanifolds and coarea formula |
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Authors: | Valentino Magnani |
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Institution: | (1) Dipartimento di Matematicà, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy |
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Abstract: | Let k be a positive integer and let m be the dimension of the horizontal subspace of a stratified group. Under the condition k ≤ 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 a.e. 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. |
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Keywords: | |
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