An Ohsawa-Takegoshi theorem on compact Kähler manifolds

Abstract

We prove two extension theorems of Ohsawa-Takegoshi type on compact Kahler manifolds. In our proof, there are many complications arising from the regularization process of quasi-psh functions on compact Kahler manifolds, and unfortunately we only obtain particular cases of the expected result. We remark that the two special cases we proved are natural, since they occur in many situations. We hope that the new techniques we develop here will allow us to obtain the general extension result of Ohsawa-Takegoshi type on compact Kahler manifolds in a near future.