The principal investigator will study several difficult problems in complex geometry. Having proved a fundamental preliminary result, the PI will now find a complete set of continuous invariants for families of complex hypersurfaces. This problem may be reduced to studing the lower dimensional case by algebraic means. The PI will also study the diffeomorphism classes of complex submanifolds with real codimension greater than three. He will use his understanding of the Kohn-Rossi cohomology to solve the complex Plateau problem. The proposed work will shed light on the difficult complex Plateau problem and on our understanding of hypersurfaces which are contained in high dimensional complex spaces. Such problems have their origins in Gauss's original studies of imaginary numbers such as the square root of -1.
