О геометрии вещественных аналитических Леви-плоских особенностей

We discuss some recent results on the geometry of real analytic Levi-flat hypersurfaces. In particular, we discuss a connexion between properites of the Levi foliation and the local polynomially convex hull near a singular point. The talk is based on the series of joint works with S.Pinchuk and R.Shafikov.