The principal investigator will study several problems in the geometry of domains in complex Euclidean space. In particular, he will investigate regularity properties of the Bergman projection operator which relates boundary behavior of holomorphic functions to their behavior on the interior of a domain. Another topic to be considered on this research project is the topology of Levi flat hypersurfaces. Both of these subjects require an analysis of the d"-operator on domains in n-dimensional complex space. This research continues the study of the geometry and analysis of functions of several complex variables. The theory of functions of one complex variable plays a central role in all branches of mathematics and physics. This research project will undertake continued research on functions of more than one variable which is analogous to the well studied classical situation. One surprising application of the research thus far has been to queuing theory which studies the order in which processes are performed.
