Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds  

作　　者：Qi’an Guan Zhitong Mi Zheng Yuan 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing,100871,China [2]School of Mathematics and Statistics,Beijing Jiaotong University,Beijing,100044,China [3]Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,100190,China

出　　处：《Science China Mathematics》2024年第7期1665-1718,共54页中国科学（数学）（英文版）

基　　金：supported by National Key R&D Program of China (Grant No. 2021YFA1003100);supported by National Natural Science Foundation of China (Grant Nos. 11825101, 11522101, and 11431013);supported by the Talent Fund of Beijing Jiaotong University;supported by China Postdoctoral Science Foundation (Grant Nos. BX20230402 and 2023M743719)。

摘　　要：In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

关 键 词：minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex K?hler manifold 

分 类 号：O174.5[理学—数学]