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 ...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.展开更多
In this paper,we present the concavity of the minimal L^(2)integrals related to multiplier ideal sheaves on the weakly pseudoconvex Kahler manifolds,which implies the sharp effectiveness results of the strong openness...In this paper,we present the concavity of the minimal L^(2)integrals related to multiplier ideal sheaves on the weakly pseudoconvex Kahler manifolds,which implies the sharp effectiveness results of the strong openness conjecture and a conjecture posed by Demailly and Kollar(2001)on weakly pseudoconvex Kahler manifolds.We obtain the relation between the concavity and the L^(2)extension theorem.展开更多
In this article,we present the concavity of the minimal L^(2) integrals related to multiplier ideals sheaves on Stein manifolds.As applications,we obtain a necessary condition for the concavity degenerating to lineari...In this article,we present the concavity of the minimal L^(2) integrals related to multiplier ideals sheaves on Stein manifolds.As applications,we obtain a necessary condition for the concavity degenerating to linearity,a characterization for 1-dimensional case,and a characterization for the equality in 1-dimensional optimal L^(2) extension problem to hold.展开更多
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)+1 种基金supported by the Talent Fund of Beijing Jiaotong Universitysupported by China Postdoctoral Science Foundation (Grant Nos. BX20230402 and 2023M743719)。
文摘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.
基金supported by National Natural Science Foundation of China (Grant Nos. 11825101, 11522101 and 11431013)
文摘In this paper,we present the concavity of the minimal L^(2)integrals related to multiplier ideal sheaves on the weakly pseudoconvex Kahler manifolds,which implies the sharp effectiveness results of the strong openness conjecture and a conjecture posed by Demailly and Kollar(2001)on weakly pseudoconvex Kahler manifolds.We obtain the relation between the concavity and the L^(2)extension theorem.
基金The first author was supported by NSFC-11825101,NSFC-11522101 and NSFC-11431013.
文摘In this article,we present the concavity of the minimal L^(2) integrals related to multiplier ideals sheaves on Stein manifolds.As applications,we obtain a necessary condition for the concavity degenerating to linearity,a characterization for 1-dimensional case,and a characterization for the equality in 1-dimensional optimal L^(2) extension problem to hold.
