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Science China Mathematics 2006年第11期49卷 1593-1598页

作者： zhou xiangyu Institute of Mathematics AMSS Beijing Chinese Academy of Sciences

Two fundamental problems on the invariant holomorphic extensions have been posed, which are naturally arose from our solution of the extended future tube conjecture and closely and deeply related to the general theory of Stein manifolds due to Cartan-Serre. In this paper, the relationship is presented between the two problems, the motivation of considering the problems, and the methods to approach the problems. We have also posed some questions and conjectures related to this two problems.

关键词： Stein manifold, group action, plurisubharmonic function, minimum principle, categorical quotient.

The Structure of Vector Bundles on Non-primary Hopf Manifolds

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Chinese Annals of Mathematics,Series B 2020年第6期41卷 929-938页

作者： Ning GAN xiangyu zhou School of Sciences Jimei Uni vers计yXiamen 361021FujianChina Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a nowhere vanishing *** is proved that in case dim(X)≥3,π*(E)is trivial if and only if E is filtrable by vector *** the structure theorem,the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.

关键词： Hopf manifolds Holomorphic vector bundles Exact sequence Cohomology Filtration Chern class

Regularization of quasi-plurisubharmonic functions on complex manifolds

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Science China Mathematics 2018年第7期61卷 1163-1174页

作者： xiangyu zhou Langfeng Zhu Institute of Mathematics Academy of Mathematics and Systems Scienceand Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences School of Mathematics and Statistics Wuhan University

In this paper, we give a survey of various regularization theorems of quasi-plurisubharmonic functions on complex manifolds, and we also discuss the ideas used in their proofs. Moreover, we will present their applicat... 详细信息

关键词： regularization theorem quasi-plurisubharmonic function multiplier ideal sheaf L2 estimate ex-tension theorem

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

The degree of biholomorphic mappings between special domains in C^n preserving 0

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Science China Mathematics 2017年第6期60卷 1077-1082页

作者： NING JiaFu zhou xiangyu College of Mathematics and Statistics Chongqing University Academy of Mathematics and Systems Science Chinese Academy of Sciences

Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mapping （see Ning et al. （2017））. In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan＇s theorem.

关键词： group action degree of polynomial mapping biholomorphic mapping Bergman kernel invariant domain

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

L^(2) EXTENSIONS WITH SINGULAR METRICS ON K?HLER MANIFOLDS

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Acta Mathematica Scientia 2021年第6期41卷 2021-2038页

作者： xiangyu zhou Langfeng ZHU Institute of Mathematics AMSSand Hua Loo-Keng Key Laboratory of MathematicsChinese Academy of SciencesBeijing100190China School of Mathematics and Statistics Wuhan UniversityWuhan430072China

In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equip... 详细信息

关键词： singular metric optimal L^(2)extension theorem strong openness of multiplier ideal sheaf generalized Siu’s lemma weakly pseudoconvex Kähler manifold

Rigidity and regularity in group actions

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Science China Mathematics 2008年第4期51卷 819-826页

作者： WU XiaoWen DENG FuSheng zhou xiangyu Department of Mathematics Zhejiang UniversityHangzhou 310027China Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100080China

Some new results on the rigidity of automorphism groups and the regularity of $ \bar \partial $ -Neumann operator in group actions are presented.

关键词： rigidity of automorphism groups regularity of █-Neumann operator transverse symmetry

Dynamics of a multiplex neural network with delayed couplings

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Applied Mathematics and Mechanics(English Edition) 2021年第3期42卷 441-456页

作者： Xiaochen MAO Xingyong LI Weijie DING Song WANG xiangyu zhou Lei QIAO Department of Engineering Mechanics College of Mechanics and MaterialsHohai UniversityNanjing 211100China

Multiplex networks have drawn much attention since they have been observed in many systems,e.g.,brain,transport,and social *** this paper,the nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is *** stability and bifurcation of the network equilibrium are discussed,and interesting neural activities of the network are *** on the neuron circuit,transfer function circuit,and time delay circuit,a circuit platform of the network is *** is shown that delayed couplings play crucial roles in the network dynamics,e.g.,the enhancement and suppression of the stability,the patterns of the synchronization between networks,and the generation of complicated attractors and multi-stability coexistence.

关键词： neural network time delay synchronization coexisting attractor

Multiple current peaks and spatial characteristics of atmospheric helium dielectric barrier discharges with repetitive unipolar narrow pulse excitation

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Plasma Science and Technology 2021年第6期23卷 21-29页

作者： xiangyu zhou Qiao WANG Dong DAI Zeen HUANG School of Electric Power South China University of TechnologyGuangzhou 510641People's Republic of China

Atmospheric dielectric barrier discharges driven by repetitive unipolar narrow pulse excitation are investigated numerically by using one-dimensional fluid *** one-dimensional simulation focuses on the effects of applied voltage amplitude,pulse repetition frequency,gap width andγcoefficient on the multiple-current-pulse(MCP)*** results indicate that the MCP behavior will lead to the stratification of electron density distribution in axial *** MCP manipulating methods,such as reducing the applied voltage amplitude,increasing the applied voltage frequency,adjusting the gap width,cannot regulate MCPs exhibiting in this *** analyses reveal that the increasing electric field of the cathode fall region is the basis for the emergence of MCP behavior.

关键词： dielectric barrier discharges narrow pulse excitation multiple-current-pulse discharge electric field cathode fall region