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

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 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.