A longstanding open problem in subRiemannian geometry deals with the regularity of minimizing geodesics of subRiemannian structures, namely it asks whether minimizing geodesics are smooth. This is the case for minimizing geodesics which are projections of normal extremals but only partial results are known for strict singular minimizing geodesics, i.e., length minimizers which are only projections of abnormal extremals. In this talk, I will first recall the main concepts at stake and then I will present the first example of a non smooth subRiemannian minimizing geodesic and explain briefly the proof structure yielding such an example. This is joint work with F. Jean, R. Monti, L. Riffors, L. Sachelli, M. Sigalotti and A. Socionovo.

报告人简介：Yacine Chitour received his PhD degree from Rugers University, USA in 1996, after graduating from Ecole Polytechnique, Palaiseau, France. He was with the mathematics department of Universite Paris-Sud， France from 1997 till 2004. Since then, he is Professor of Control Theory at Universite Paris-Saclay, France, a member of Laboratoire des signaux et systemes. Since 2018 he is a member of Institut Uiniversitaire de France. His interests are geometric and optimal control, delay and switched systems, sliding mode and control of partial differential equations with application to robotics and neurosciences.