Mathematical Sciences: Asymptotic Behavior and the SingularSet of Minimal Surfaces and Harmonic Maps

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The principal investigators will study geometric variational problems and singularities of solutions. Professor Simon will concentrate his research on the structure of the singular set of minimal surfaces and harmonic maps. He will also consider asympotics on approach to singular points including the unique tangent cone problem. Professor White will investigate the bridge theorem for minimal surfaces, branch points in minimal surfaces, uniqueness of tangent cones and tangent maps in minimal varieties and harmonic maps. 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.