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

Abstract

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