Bounding smooth Levi-flat hypersurfaces 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 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 $\hat{M}$ that is foliated by Stein hypersurfaces diffeomorphic to the ball. Moreover, $\hat{M}$ is the hull of holomorphy of $M$. This is based on a joint work with H. Fang, X.Huang and W.Yin. Time permitting, I will discuss work in progress regrading generalizations to hyperbolic singularities.