On measures in sub-Riemannian geometry

R Ghezzi (1) , Frédéric Jean (2)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 OC - Optimisation et commande

In \cite{gjha} we give a detailed analysis of spherical Hausdorff measures on sub-Riemannian manifolds in a general framework, that is, without the assumption of equiregularity. The present paper is devised as a complement of this analysis, with both new results and open questions. The first aim is to extend the study to other kinds of intrinsic measures on sub-Riemannian manifolds, namely Popp's measure and general (i.e., non spherical) Hausdorff measures. The second is to explore some consequences of \cite{gjha} on metric measure spaces based on sub-Riemannian manifolds.

Domaines: Géométrie métrique [math.MG]; Géométrie différentielle [math.DG]; Optimisation et contrôle [math.OC]

R Ghezzi, Frédéric Jean. On measures in sub-Riemannian geometry. 2017. ⟨hal-01452778v1⟩