Abstract: The existence of sub-Riemannian geodesics of abnormal type (i.e.
singular in the sense of Pontryagin Maximum Principle) has been
established by R.Montgomery in 1994. The regularity of such curves is
still unknown for general sub-Riemannian manifolds. In this talk, a
regularity theorem concerning the elimination of corner-like
singularities for length minimizing curves will be presented, as well as
some corollaries. This theorem holds for a large class of equiregular
sub-Riemannian manifolds and is based on a new iterative construction,
aimed to finely control the end-point of an abnormal geodesic via small
perturbations.