Research Interests

My research interests concern the theory of several complex variables, differential geometry, and algebraic geometry, especially problems in their interfaces. I have worked on the theory of extending analytic objects, such as meromorphic maps and coherent analytic sheaves, across subvarieties or pseudoconcave boundaries and have described the structure of closed positive currents in terms of subvarieties. I introduced Bochner-Kodaira techniques to harmonic maps to develop the theory of geometric strong rigidity and super-rigidity of Kahler and Riemannian manifolds. I apply the estimates of the complex Neumann problem and the theory of multiplier ideal sheaves to algebraic geometry to study and resolve conjectures such as the deformational invariance of the plurigenera and to obtain effective results such as the effective multiple needed for an ample line bundle to be very ample or for its adjoint bundle to be globally generated. I use function-theoretical and algebraic geometric techniques to investigate and solve problems in value distribution theory and the theory of hyperbolicity in complex geometry.

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Primary Section

Section 11: Mathematics