Sub-Riemannian abnormal extremals

Abstract

The abnormal extremals are the obstruction to regularity of sub-Riemannian geodesics. Even in the case of 3-dimensional analytic sub-Riemannian manifolds it was only relatively recently shown by Belotto da Silva, Figalli, Parusiński and Rifford that also the abnormal geodesics are at least C^1. In this talk I will cover some regularity results using a metric approach based on joint work with Enrico Le Donne, and cover some results studying how complicated the singularities of abnormal extremals can be.