Mathematical Sciences: Differential Geometry and Partial Differential Equations

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The principal investigator will continue his research on geometric variation problems. He will study stability and holomorphicity properties of minimal surfaces in arbitrary codimension, and develop existence theory for Lagrangian minimal submanifolds of Kahler-Einstein manifolds. He will also study the structure of harmonic maps into singular spaces of nonpositive curvature and determine general conditions under which the Bochner method can be used to establish rigidity theorems. 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.