Entire and Meromorphic Functions in Several Complex Variables

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ABSTRACT Bao Qin Li Li will study necessary and sufficient geometric conditions for an analytic variety to be an interpolating variety for weighted spaces of entire functions. In a second direction, he will use results and methods of interpolation to study exponential polynomials and obtain Lojasiewicz type inequalities, which are tied to some important conjectures in complex and harmonic analysis. In a third direction, he plans to find estimates on the volume of zero varieties for entire holomorphic maps, which are closely related to geometric aspects of interpolating varieties. He will also study the "refined" Nevanlinna second fundamental theorem for moving targets, with special attention given to uniqueness problems of meromorphic functions and meromorphic solutions of (partial) differential equations. Many important problems like finding all distribution solutions (or finding out whether there are any) to systems of convolution equations arising in signal processing, image compression, and other applications can be translated to interpolation problems for entire functions with growth conditions. The topic itself is one of the major problems in several complex variables. The proposed research has as its goal to enrich and advance the above areas in several complex variables and their applications.