Liouville's theorem and the maximum modulus principle for a system of complex vector fields

Abstract

This work is concerned with Liouville's theorem and the maximum principle for the homogeneous solutions of systems of complex vector fields . Necessary and sufficient conditions are provedfor tube structures to have the Liouville property. Maximum principles are proved for a general system of complex vector fields which are integrable. As an application, in the case of vector fields, we get new characterizations of the local solvability property (P) of Nirenberg andTreves. Another application concerns a solvability condition (Pn-1) introduced by P.Cordaro and J. Hounie in differential complexes associated to locally integrable structures.