Mathematical Sciences: Local and Global Geometry
James Faran Principal Investigator
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The principal investigator will use his characterization of the Kobayashi metric on smoothly bounded convex domains to study the asymptotic behavior of this metric at a boundary. The ultimate goal is to solidify the relationship between complex function theory on the domain and the geometry of the boundary. In a second project he will study the global properties of contact structures on manifolds of dimension three. Topological invariants of the contact structure will be constructed analytically. Many of the most significant theorems in geometric analysis relate geometric and topological invariants. One of the earliest of these was the relationship between the total Gaussian curvature of a smooth surface and its numbers of tubes and cross caps. In the present project, the principal investigator will relate global Riemannian contact structures to the base topology of the manifold.