Optimal L 2 Extensions of Openness Type and Related Topics

Abstract

We establish several optimal L 2 extension theorems of openness type on weakly pseudoconvex Kähler manifolds. We prove a product property for certain minimal L 2 extensions, which generalizes the product property of Bergman kernels. We describe a different approach to the Suita conjecture and its generalizations, which is based on a log-concavity for certain minimal L 2 integrals.