Regularity of minimal intrinsic graphs in 3 dimensional sub-Riemannian structures of step 2

This work provides a characterization of the regularity of noncharacteristic intrinsic minimal graphs for a class of vector fields that includes non nilpotent Lie algebras as the one given by Euclidean motions of the plane. The main result extends a previous one on the Heisenberg group, using similar techniques to deal with nonlinearities. This wider setting provides a better understanding of geometric constraints, together with an extension of the potentialities of specific tools as the lifting-freezing procedure and interpolation inequalities. As a consequence of the regularity, a foliation result for minimal graphs is obtained.