Sard Theorem for the endpoint map in some sub-Riemannian manifolds

Abstract: 

SubRiemannian geometries occur in many areas of pure and applied mathematics, including PDEs, several complex variables, control theory, non-holonomic mechanical systems, and neurobiology. We introduce subRiemannian manifolds and give some examples. Therefore we discuss some open problems, and in particular we focus on the Sard Theorem for the endpoint map. This is related to the study of length minimizers, and we consider some new results obtained on this problem in collaboration with E. Le Donne, R. Montgomery, P. Pansu and D. Vittone.