Geometric and Analytic Problems on Real Hypersurfaces

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Functions of complex variables play an essential role throughout much of mathematics and in many parts of physics and engineering. This project will develop a number of interrelated topics in complex variables theory which may serve to open up new directions within that theory and to build bridges from that theory to other mathematical areas. It is expected that the project will help to build human infrastructure by involving students and younger investigators.The specific problems to be addressed by the principal investigator include geometric and variational problems connected to Fefferman measure and Webster curvature; the study of partial differential equations serving as boundary compatibility conditions for various overdetermined boundary value problems arising in several complex variables; the study of competing partial complex structures on boundaries of certain complex euclidean domains arising from considerations of projective duality; the study of constants for of Poincare-type inequalities on Hardy spaces; and the study of boundary norms for solutions of holomorphic constant-coefficient partial differential equations.