Abnormals and cut loci (Q1776267)

We study the regularity properties of sub-Riemannian distances and their interrelations with abnormal extremals. The existence of singular minimizers makes the study of sub-Riemannian distances rather complicated. It is known that these distances are not C1 in a neighborhood of a point reached by an abnormal minimizer [\textit{S. Jaquet}, J. Dyn. Control Syst. 5, No. 3, 303--328 (1999; Zbl 0963.53014)] and may also fail to be subanalytic [\textit{A. A. Agrachev, B. Bonnard, M. Chyba} and \textit{I. Kupka}, ESAIM, Control Optim. Calc. Var. 2, 377--448 (1997; Zbl 0902.53033)].