A converse of Hormander''''s L^(2)-estimate and new positivity notions for vector bundles

摘要

We study conditions of Hormander''s L^(2)-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the Hormander-type condition,we show a converse of Hormander''s L^(2)-estimate under some regularity assumptions on an n-dimensional domain.This result is a partial generalization of the one-dimensional result obtained by Berndtsson(1998).We also define new positivity notions for vector bundles with singular Hermitian metrics by using these conditions.We investigate these positivity notions and compare them with classical positivity notions.