【摘 要】
：
We study conditions of H?rmander\'s L2-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the H?rmander-type condition,we show a converse of H?rmander\'s L2-estimate under some regularity assumptions on an n-dimension
【机 构】
：
Mathematical Institute,Tohoku University,Sendai 980-8578,Japan;Graduate School of Mathematical Scien
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We study conditions of H?rmander\'s L2-estimate and the Ohsawa-Takegoshi extension theorem.Introducing a twisted version of the H?rmander-type condition,we show a converse of H?rmander\'s L2-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.
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