Mathematical Sciences: Four Projects in Geometric Analysis

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This grant supports a program of research in geometric analysis undertaken by the principal investigators over the next two years. The proposal consists of four projects. (1) Singular phenomena in analytic partial differential equations; (2) Lorentzian geometry; (3) Geometry related to the Gauss map; (4) Grassman manifolds and Convexity theory. In each of the projects, the investigations will proceed from known special cases to more general situations. Common themes for some of these projects are the interrelationships in the various notions of Gauss maps. Some of the topics are in early exploratory stage. Studies in geometric analysis are of fundamental importance to our understanding of the physical world and models described by partial differential equations.