Mathematical Sciences: "Complex Manifolds and Meromorphic Mappings"

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This project continues work on problems centering on functions of several complex variables. The research uses geometric measure theory in complex analysis to characterize holomorphic chains in terms of locally rectifiable currents. Work will also be done on Hartogs-type theorems concerned with almost-everywhere separately meromorphic functions. Investigations will be carried out on value distribution theory of functions of several complex variables. The second main theorem and defect relations for non-equidimensional meromorphic mappings into complex projective manifolds will also be treated. Work on cohomology vanishing results for holomorphic line bundles satisfying weak numerical positivity conditions on complex projective manifolds will be carried out. Efforts will be made to construct semi-positive metrics on these line bundles. This research will provide valuable tools for studies in mappings between hypersurfaces.