DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, February 28 Padelford C-36 3:45 PM

Edge of the wedge theory in hypo-analytic manifolds

Robin Graham (UW)

The subject of extending CR functions defined on submanifolds of ℂ^{n} to open sets nearby has a rich history. This talk will describe joint work with Michael Eastwood developing an edge of the wedge theory in generic CR submanifolds of ℂ^{n}, or more generally, in hypo-analytic manifolds. The general results are formulated in terms of the hypo-analytic wave-front set of Baouendi-Chang-Treves. When applied to CR submanifolds, the results are of the form that if a CR function f on a given CR submanifold is the boundary value of a CR function on a wedge in a larger CR submanifold, then f is actually the boundary value of a holomorphic function in a wedge in ℂ^{n}, with precise description of the directions of the wedges involved.