TITLE: Open problems in sub-Riemannian geometry
QUESTION [7 upvotes]: What are some open problems in sub-Riemannian geometry?
I am interested especially in problems concerning connections and curvature, but any contribution is welcomed.

REPLY [5 votes]: Andrei Agrachev recently posted an article on the arXiv:  http://arxiv.org/abs/1304.2590 entitled "Some open problems" that you might find interesting.  He discusses several  open problems in control theory and sub-Riemannian geometry that are of considerable interest.