Sub-Riemannian geodesics: the cornerless area gets extended

In the sub-Riemannian geometry (the positive definite metric declared only in a subbundle in the tangent bundle) there appear so-called strictly abnormal extremals, discovered in 1991 by R. Montgomery. Many of them are with corners. On the other hand, strictly abnormal extremals need not actually minimize the sR distance/length. A vast standing question is whether a corny extremal may happen to be an sR-geodesic. A new Italian school of geometers contributes a step towards an answer.