Volume measures in non equiregular sub-Riemannian manifolds

volume
manifolds
measures
Grenoble
[MATH]Mathematics [math]
sub-riemannian
sous-riemannien
sub-riemannian days 2017
journées sous-riemanniennes 2017
non equiregular

Appears in collection : Journée sous-riemannienne 2017

In this talk we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it to a smooth volume. First we give the Lebesgue decomposition of the Hausdorff volume. Then we focus on the regular part, show that it is not commensurable with a smooth volume and give conditions under which it is a Radon measure. Finally we give a complete characterization of the singular part. This is a joint work with F. Jean (ENSTA).