Mathematical Sciences: Geometric Superrigidity and Compactification of Kahler Manifolds

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The principal investigator will study geometric rigidity and related problems from harmonic maps. The Kodaira-Bochner formulae on submanifolds will be related to the formulae on the ambient manifold. In addition the principal investigator will continue his work on compactification of Kahler manifolds that satisfy certain curvature conditions. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.