On the role of abnormal minimizers in sub-Riemannian geometry
  Consider a sub-Riemannian geometry $(U,D,g)$ where $U$ is a neighborhood at 0 in $\R^n,$ $D$ is a rank-2 smooth $(C^\infty $ or $C^\omega)$ distribution and $g$ is a smooth metric on $D$. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry. 
Bernard Bonnard (IMB), Emmanuel Tr\'elat (IMB)