Finite Type Monge-Ampère Foliations

Abstract

In this paper we extend our previous work on singularities of Monge-Ampère foliations to the case of pseudoconvex finite type domains. We are able to answer the questin of Burns on homogeneous polynomials whose logarithm satisfies the complex Monge-Ampère equation completely in dimension 2 . We are also able to generalize the work of P.M. Wong in dimension 2 on the classification of complete weighted circular domains to include finite type domains.