Inserted: 10 mar 2014
Last Updated: 25 jul 2017
Journal: ESAIM Control Optim. Calc. Var.
We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results of $$. As an application of our main result we complete and simplify the analysis in $$, showing that in a $4$-dimensional sub-Riemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth.