Abstract
In the present paper, we’ll give a survey of our recent results on the L 2 extension problem with optimal estimate. We’ll consider the problem in various settings according to Ohsawa’s series papers, and present our optimal versions of Ohsawa’s L 2 extension theorems. We’ll discuss the problem in a general setting and present a solution of the problem in the general setting. We’ll give some applications of our results including a solution of the equality part of Suita’s conjecture. Finally, we present our recent solutions of Demailly’s strong openness conjecture on multiplier ideal sheaf and related problems.
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