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Non-horizontal submanifolds and coarea formula

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Journal d'Analyse Mathématique Aims and scope

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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Authors and Affiliations

  1. Dipartimento di Matematicà, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127, Pisa, Italy

    Valentino Magnani

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  1. Valentino Magnani
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Correspondence to Valentino Magnani.

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Magnani, V. Non-horizontal submanifolds and coarea formula. J Anal Math 106, 95–127 (2008). https://doi.org/10.1007/s11854-008-0045-1

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  • DOI: https://doi.org/10.1007/s11854-008-0045-1

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