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# Xiaojun Huang, Bounding a Levi-flat Hypersurface in a Stein Manifold

## August 22 @ 4:00 pm - 5:00 pm KST

B236-1,
IBS
Korea, Republic of

*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 suppose CR points are non-minimal. Assume further that *M* is contained in a bounded strongly pseudoconvex domain. Then *M* bounds a unique smooth up to *M* Levi flat hypersurface *M̂* that is foliated by Stein subspace diffeomorphic to the ball. Moreover, *M̂* is the hull of holomorphy of *M*. This subject has a long history of investigation from E. Bishop and Harvey-Lawson. I will discuss both the history and techniques used in the proof of the above mentioned theorem.