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

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

2011-11-02

arxiv.org/abs/1111.0666v1

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.matpur.2011.04.006

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.

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