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Concavity of minimal L^(2) integrals related to multiplier ideal sheaves on weakly pseudoconvex Kahler manifolds

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Science China Mathematics 2022年第5期65卷 887-932页

作者： Qi'an Guan Zhitong Mi School of Mathematical Sciences Peking UniversityBeijing 100871China Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

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.

关键词： multiplier ideal sheaf plurisubharmonic function weakly pseudoconvex Kahler manifold sublevel set

Stability of Multiplier Ideal Sheaves

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Chinese Annals of Mathematics,Series B 2022年第5期43卷 819-832页

作者： Qi'an GUAN Zhenqian LI Xiangyu ZHOU School of Mathematical Sciences Peking UniversityBeijing 100871China Siwuge Technology Co.Ltd. Tianfu Life Science ParkChengdu 610093China Institute of Mathematics AMSSand Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing100190China

In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.

关键词： plurisubharmonic function Multiplier ideal sheaf Strong openness and stability Coherent analytic sheaf L^(2)estimate

Strong openness of multiplier ideal sheaves and optimal L^2 extension

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Science China Mathematics 2017年第6期60卷 967-976页

作者： GUAN Qi'An ZHOU XiangYu School of Mathematical Sciences Peking University Beijing 100871 China Beijing International Center for Mathematical Research Peking University Beijing 100871 China Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Hua Loo-Kcng Key Laboratory of Mathematics Chinese Academy of Sciences Beijing 100190 China

In this paper, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll′ar and Jonsson-Mustat?a implies the truth of twisted versions of the strong openness conjecture; our optimal L^2 extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.

关键词： strong openness conjecture plurisubharmonic function multiplier ideal sheaf optimal L^2 extension theorem

A general extension theorem for cohomology classes on non reduced analytic subspaces

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Science China Mathematics 2017年第6期60卷 949-962页

作者： CAO JunYan DEMAILLY Jean-Pierre MATSUMURA Shin-ichi Institut de Mathématiques de Jussieu UniversitéPierre et Marie CurieParis 75252France Institut Fourier UniversitéGrenoble AlpesGlares 38610France Mathematical Institute Tohoku UniversitySendal 980-8578Japan

The main purpose of this paper is to generalize the celebrated L^2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.

关键词： compact Khler manifold singular hermitian metric coherent sheaf cohomology Dolbeault cohomology plurisubharmonic function L^2 estimates Ohsawa-Takegoshi extension theorem multiplier ideal sheaf

Characterizations of plurisubharmonic functions

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Science China Mathematics 2021年第9期64卷 1959-1970页

作者： Fusheng Deng Jiafu Ning Zhiwei Wang School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049China School of Mathematics and Statistics HNP-LAMA Central South UniversityChangsha410083China Laboratory of Mathematics and Complex Systems(Ministry of Education) School of Mathematical SciencesBeijing Normal UniversityBeijing100875China

We give characterizations of(quasi-)plurisubharmonic functions in terms of L^(p)-estimates of■and Lp-extensions of holomorphic functions.

关键词： plurisubharmonic function H?rmander’s L2-estimate Ohsawa-Takegoshi extension theorem characterization of plurisubharmonicity

A Class of plurisubharmonic functions of Positively Homogeneous of Order ρ

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Systems Science and Systems Engineering 2000年第1期10卷 110-118页

作者： WANG Guang Department of Mathematics, Shanxi University, Taiyuan 030006,China

In this paper, we construct and discuss some plurisubharmonic functions of positively homogeneous of oder ρ and some weight system, which will be used in the study of the solution of Dirichlet problem for the com... 详细信息

关键词： plurisubharmonic function weight system Monge\|Ampère equation support function

APPLICATIONS OF THE DIVISION PROBLEM IN SPACES OF ENTIRE functionS

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Systems Science and Systems Engineering 2003年第3期12卷 307-313页

作者： Guang WANGDepartment of Mathematics Shanxi University, Taiyuan 030006, P.R.China Department of Mathematics Shanxi University Taiyuan 030006 P.R.China

Based on the results of (Wang 2001), we give some applications of division problem in spaces of entire functions of finite type. Especially, when p = 1 and H is the support functions of a bounded convex domain of C , ... 详细信息

关键词： Entire function plurisubharmonic function weight system division problem

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关于有界集的解析RNP的一刻划

Northeastern Mathematical Journal 1996年第2期12卷 227-229页

作者：步尚全

A new characterization of the analytic Radon-Nikodym property for boounded subsets in complex Banach spaces is given.

关键词： plurisubharmonically Dentable Subset Analytic Radon-Nikodym Property plurisubharmonic function