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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

Quaternionic Monge–Ampère Measure on Pluripolar Set

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1431-1457页

作者： Hichame AMAL Saïd ASSERDA Fadoua BOUKHARI Department of Mathematics Laboratory LaREAMIRegional Centre of Trades of Education and TrainingKenitraMorocco Ibn Tofail University Faculty of SciencesDepartment of MathematicsPO 242 KenitraMorroco

In this paper, we prove that in a hyperconvex domain Ω in H^(n), if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure, then it is a quaternionic Monge–Ampère measure of a function i... 详细信息

关键词： Quaternion space Monge-Amp`ere operator plurisubharmonic function

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 Kahler manifold singular hermitian metric coherent sheaf cohomology Dolbeault coho- mology plurisubharmonic function L2 estimates Ohsawa-Takegoshi extension theorem multiplier ideal sheaf

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 *** 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

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

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

Concavity of Minimal L^(2) Integrals Related to Multiplier Ideal Sheaves

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Peking Mathematical Journal 2023年第2期6卷 393-457页

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

In this article,we present the concavity of the minimal L^(2) integrals related to multiplier ideals sheaves on Stein *** 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.

关键词： Strong openness conjecture Multiplier ideal sheaf plurisubharmonic function Sublevel set

Concavity Property of Minimal L^(2)Integrals with Lebesgue Measurable GainⅣ:Product of Open Riemann Surfaces

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Peking Mathematical Journal 2024年第1期7卷 91-154页

作者： Qi’an Guan Zheng Yuan School of Mathematical Sciences Peking UniversityBeijing 100871China

In this article,we present characterizations of the concavity property of minimal L^(2)integrals degenerating to linearity in the case of products of analytic subsets on products of open Riemann *** applications,we obtain characterizations of the holding of equality in optimal jets L^(2)extension problem from products of analytic subsets to products of open Riemann surfaces,which implies characterizations of the product versions of the equality parts of Suita conjecture and extended Suita conjecture,and the equality holding of a conjecture of Ohsawa for products of open Riemann surfaces.

关键词： plurisubharmonic function Multiplier ideal sheaf Minimal L^(2)integral Concavity Optimal L^(2)extension theorem

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 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