Strong openness of multiplier ideal sheaves and optimal L2 extension
Abstract
In this note, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll\'ar and Jonsson-Mustata implies the truth of twisted versions of the strong openness conjecture; our optimal L2 extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.
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