On the Spherical Hausdorff Measure in Step 2 Corank 2 sub-Riemannian Geometry

Ugo Boscain (1) , Jean-Paul Gauthier (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LSIS - Laboratoire des Sciences de l'Information et des Systèmes

In this paper, we consider generic corank 2 sub-Riemannian structures, and we show that the Spherical Hausdorf measure is always a C^1-smooth volume, which is in fact generically C^2- smooth out of a stratified subset of codimension 7. In particular, for rank 4, it is generically C^2 . This is the continuation of a previous work by the auhors.

Mots clés: optimal control; sub-Riemannian geometry

Domaines: Géométrie différentielle [math.DG]

Ugo Boscain, Jean-Paul Gauthier. On the Spherical Hausdorff Measure in Step 2 Corank 2 sub-Riemannian Geometry. 2012. ⟨hal-00739965⟩