Mathematical Sciences: Problems in Complex Analysis

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The principal investigator will continue his study of C-R geometry and holomorphic maps. He will use methods from analysis such as estimates for the d"-operator as well as geometric techniques including folliations determined by the Monge-Ampere operator. In another direction, the principal investigator will study iterations of polynomial maps in several complex variables. He will continue his investigation of properties of Julia sets and the ergodic properties of the maps. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.