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.
Regularity of non charachteristic minimal graphs in Lie groups of step 2 and dimension 3 / Barbieri D.; Citti G. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 96:(2011), pp. 279-306. [10.1016/j.matpur.2011.04.006]
Regularity of non charachteristic minimal graphs in Lie groups of step 2 and dimension 3
BARBIERI, DAVIDE;CITTI, GIOVANNA
2011
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.