Title:

On Levi-flat CR manifolds from the point of view of positive normal bundles

Abstract:

The study of Levi-flat CR manifolds is related to basic questions in different research areas such as theory of foliations, dynamical systems, complex algebraic geometry and several complex variables. I will discuss some recent results within the general aim of classifying compact Levi-flat CR manifolds, in particular from the point of view of positive normal bundles. Essential ingredients of the proofs are vanishing results for some analytic cohomology classes by means of weighted $L^2$-methods for solving $\overline\partial$- equations.