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

TL;DR

This paper characterizes the regularity of noncharacteristic intrinsic minimal graphs in 3D sub-Riemannian structures of step 2, extending previous results from the Heisenberg group to more general settings.

Contribution

It extends regularity results for minimal graphs from the Heisenberg group to a broader class of sub-Riemannian structures, including non nilpotent Lie algebras.

Findings

Regularity of minimal graphs is established in new sub-Riemannian settings.

A foliation result for minimal graphs is derived.

Techniques include lifting-freezing procedures and interpolation inequalities.

Abstract

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.