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Embeddings and deformations of three-dimensional CR manifolds.

Peter Ebenfeld (UCSD)

Location:  Hill 705
Date & time: Friday, 14 February 2020 at 4:00PM - 5:00PM

Abstract: It is a classical result by L. Boutet de Movel that any compact strictly pseudoconvex (hypersurface type) CR manifold of dimension strictly greater than 3 is embeddable in \(\mathbb{C}^n\) for some \(n\). For strictly pseudoconvex CR manifold of dimension 3, the situation is more subtle. It is known that “most” are not embeddable. A characterization of embeddability in terms of a closed range property of \(\bar\partial\) was given by J. Kohn. In this talk, we shall discuss the embeddability problem for strictly pseudoconvex CR 3-folds in more geometric terms. The approach will be to realize the embeddable deformations of an already embedded CR 3-fold as a geometric flow in complex space.