Entire and Meromorphic Functions in Several Complex Variables

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The proposed research is directed at topics in several complex variables onentire holomorphic maps, interpolation problems, and value distribution theory.The principle investigator proposes to continue his study on the well-knowntranscendental Bezout problem about the growth of the volume of entire analyticsets and find sharp estimates on the counting functions of zeros of entireholomorphic maps. He also proposes to study interpolation problems for weighted spaces of entire functions, one of fundamental and central problems in several complex variables. In particular, he wishes to characterize interpolatingvarieties geometrically, which is closely tied with his study on the Bezoutproblem. In the third direction, he would like to continue his research on valuedistribution theory with a special attention given to the refined Nevanlinnasecond fundamental theorem for slowly moving targets and its relations to otherproblems such as uniqueness problems of meromorphic functions and meromorphic solutions of partial differential equations.The above problems are important not just from the point of view of severalcomplex variables, but also from their relations and applications to othersubjects such as harmonic analysis, transcendental number theory, systems theory and engineering. For instance, many important problems like finding andrepresenting solutions to partial differential equations or systems ofconvolution equations arising in signal processing, image compression, materialstesting, etc. are equivalent to interpolation problems for entire functions inweighted spaces. The proposed research aims at developing and advancing boththeories and applications for the above areas in several complex variables.