Regularity of minimal intrinsic graphs in 3 dimensional sub-Riemannian structures of step 2
Analysis of PDEs
2011-11-04 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1111.0666,
title = {Regularity of minimal intrinsic graphs in 3 dimensional sub-Riemannian structures of step 2},
author = {Davide Barbieri and Giovanna Citti},
journal= {arXiv preprint arXiv:1111.0666},
year = {2011}
}