Mathematical Sciences: Research in Complex Analysis

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The principal investigator will continue his study of questions involving functions of several complex variables related to potential theory, dynamical systems and holomorphic mapping. With regard to potential theory, he will study properties of the complex Monge-Ampere operator and its relationship to the stability of the Dirichlet problem and to the pluri-complex Green function. With regard to dynamical systems, he will study the behavior of invertible polynomial mappings of complex Euclidean space, especially the equilibrium measure of the analog of the Julia set. And with regard to holomorphic mappings, he will try to classify the smoothly bounded domains that have noncompact automorphism groups.