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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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