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 $C^1$.

20 pages, v2 minor corrections, to appear on J. Math. Pures Appl