Department of Mathematics,
University of California San Diego
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Math 248: Real Analysis Seminar
Professor Xiaojun Huang
Rutgers University - New Brunswick
Bounding a Levi-flat Hypersurface in a Stein Manifold
Abstract:
Let M be a smooth real codimension two compact submanifold in a Stein manifold. We will prove the following theorem: Suppose that M has two elliptic complex tangents and that CR points are non-minimal. Assume further that M is contained in a bounded strongly pseudoconvex domain. Then M bounds a unique smoothly up to M Levi-flat hypersurface $\widehat{M}$ that is foliated by Stein hyper-surfaces diffeomorphic to the ball. Moreover, $\widehat{M}$ is the hull of holomorphy of M . This subject has a long history of investigation dating back to E. Bishop and Harvey-Lawson. I will discuss both the historical context and the techniques used in the proof of the aforementioned theorem.
Hosts: Peter Ebenfelt and Ming Xiao
April 17, 2025
2:00 PM
APM 7218
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