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

作　　者：Genki Hosono Takahiro Inayama 

机构地区：[1]Mathematical Institute,Tohoku University,Sendai 980-8578,Japan [2]Graduate School of Mathematical Sciences,The University of Tokyo,Tokyo 153-8914,Japan

出　　处：《Science China Mathematics》2021年第8期1745-1756,共12页中国科学：数学（英文版）

基　　金：supported by the Program for Leading Graduate Schools,the Ministry of Education,Culture,Sports,Science and Technology,Japan,and Japan Society for the Promotion of Science,Grants-in-Aid for Scientific Research(Grant No.18J22119)。

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.

关 键 词：L^(2)-estimate singular Hermitian metrics Ohsawa-Takegoshi L^(2)-extension theorems 

分 类 号：O186.1[理学—数学]