A. Agrachev, Any sub-Riemannian metric has points of smoothness, Doklady Mathematics, vol.79, issue.1, pp.295-29845, 2009.
DOI : 10.1134/S106456240901013X

A. Agrachev, D. Barilari, and U. Boscain, Introduction to Riemannian and sub- Riemannian geometry
DOI : 10.4171/163-1/1

A. Agrachev and P. Lee, Optimal transportation under nonholonomic constraints, Transactions of the American Mathematical Society, vol.361, issue.11, pp.6019-6047, 2009.
DOI : 10.1090/S0002-9947-09-04813-2
URL : http://arxiv.org/abs/0710.0408

A. Agrachev and P. Lee, Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds, Mathematische Annalen, vol.259, issue.1, 2009.
DOI : 10.1007/s00208-014-1034-6
URL : http://arxiv.org/abs/0903.2550

V. Arnold, Sur la g??om??trie diff??rentielle des groupes de Lie de dimension infinie et ses applications ?? l'hydrodynamique des fluides parfaits, Annales de l???institut Fourier, vol.16, issue.1, pp.319-361, 1966.
DOI : 10.5802/aif.233
URL : http://archive.numdam.org/article/AIF_1966__16_1_319_0.pdf

A. Bella¨?chebella¨?che, The tangent space in sub-Riemannian geometry, pp.1-78, 1996.

P. Cannarsa and L. Rifford, Semiconcavity results for optimal control problems admitting no singular minimizing controls??????This research was completed, in part, while the first author was visiting the Universit?? de Lyon 1 and, in part, while the second author was visiting the Universit?? di Roma Tor Vergata on an INdAM grant. The authors are grateful to the above institutions for their support., Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.25, issue.4, pp.773-802, 2008.
DOI : 10.1016/j.anihpc.2007.07.005

P. Cannarsa and C. Sinestrari, Semiconcave functions, Hamilton-Jacobi equations, and optimal control, Progress in Nonlinear Differential Equations and their Applications, 2004.

M. Castelpietra and L. Rifford, Regularity properties of the distance functions to conjugate and cut loci for viscosity solutions of Hamilton-Jacobi equations and applications in Riemannian geometry, ESAIM: Control, Optimisation and Calculus of Variations, vol.16, issue.3, pp.695-718, 2010.
DOI : 10.1051/cocv/2009020
URL : https://hal.archives-ouvertes.fr/hal-00923303

A. Figalli and L. Rifford, Mass Transportation on Sub-Riemannian Manifolds, Geometric and Functional Analysis, vol.11, issue.2, pp.124-159, 2010.
DOI : 10.1007/s00039-010-0053-z
URL : https://hal.archives-ouvertes.fr/hal-00541484

S. Gallot, D. Hulin, and J. Lafontaine, Riemannian geometry, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00002870

C. Golé and R. Karidi, A note on Carnot geodesics in nilpotent Lie groups, Journal of Dynamical and Control Systems, vol.24, issue.4, pp.535-549, 1995.
DOI : 10.1007/BF02255895

M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, vol.152, 1999.

J. Itoh and M. Tanaka, The Lipschitz continuity of the distance function to the cut locus, Transactions of the American Mathematical Society, vol.353, issue.01, pp.21-40, 2001.
DOI : 10.1090/S0002-9947-00-02564-2

N. Juillet, Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group, International Mathematics Research Notices, vol.13, pp.2347-2373, 2009.
DOI : 10.1093/imrn/rnp019

N. Juillet, On a method to disprove generalized Brunn-Minkowski inequalities, Probabilistic approach to geometry, pp.189-198, 2010.

E. and L. Donne, Lecture notes on sub-Riemannian geometry, 2010.

Y. Li and L. Nirenberg, The distance function to the boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations, Communications on Pure and Applied Mathematics, vol.15, issue.1, pp.85-146, 2005.
DOI : 10.1002/cpa.20051

J. Lott and C. Villani, Weak curvature conditions and functional inequalities, Journal of Functional Analysis, vol.245, issue.1, pp.311-333, 2007.
DOI : 10.1016/j.jfa.2006.10.018
URL : http://doi.org/10.1016/j.jfa.2006.10.018

J. Milnor, Curvatures of left invariant metrics on lie groups, Advances in Mathematics, vol.21, issue.3, pp.293-329, 1976.
DOI : 10.1016/S0001-8708(76)80002-3

J. Mitchell, On Carnot-Carath??odory metrics, Journal of Differential Geometry, vol.21, issue.1, pp.35-45, 1985.
DOI : 10.4310/jdg/1214439462

R. Montgomery, A tour of sub-Riemannian geometries, their geodesics and applications, Mathematical Surveys and Monographs, vol.91, 2002.

S. Ohta, On the measure contraction property of metric measure spaces, Commentarii Mathematici Helvetici, vol.82, issue.4, pp.805-828, 2007.
DOI : 10.4171/CMH/110

L. Rifford, Sub-Riemannian Geometry and Optimal Transport, 2012.
DOI : 10.1007/978-3-319-04804-8
URL : https://hal.archives-ouvertes.fr/hal-01131787

K. Sturm, On the geometry of metric measure spaces, Acta Mathematica, vol.196, issue.1, pp.65-131, 2006.
DOI : 10.1007/s11511-006-0002-8

K. Sturm, On the geometry of metric measure spaces, Acta Mathematica, vol.196, issue.1, pp.133-177, 2006.
DOI : 10.1007/s11511-006-0002-8

C. Villani, Optimal transport, Old and New, Grundlehren der Mathematischen Wissenschaften, 2009.