Application of the group foliation method to the complex Monge-Ampère equation

Abstract

We apply the method of group foliation to the complex Monge-Ampere equation (CMA2) to establish a regular framework for finding its non-invariant solutions. We employ an infinite symmetry subgroup ofCMA2 to produce a foliation of the solution space into orbits of solutions with respect to this group and a corresponding splitting ofCMA2 into an automorphic system and a resolvent system. We propose a new approach to group foliation which is based on the commutator algebra of operators of invariant differentiation. This algebra together with its Jacobi identities provides the commutator representation of the resolvent system.