On the regularity of abnormal minimizers for rank $2$ sub-Riemannian structures

Abstract

We prove the $C^1$ regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class $C^1$.

Publication
Preprint