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Boundary Points,Minimal L^(2)Integrals and Concavity PropertyⅢ—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces: 《Acta Mathematica Sinica,English Series》2024年第9期2091-2152,共62页Qi An GUAN Zhi Tong MI Zheng YUAN; supported by National Key R&D Program of China(Grant No.2021YFA1003100);supported by NSFC(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)。; In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified version.As...; 关键词：Minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex Kähler manifold

Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains: 《Science China Mathematics》2024年第8期1827-1864,共38页Xiaoshu Ge Chunping Zhong; supported by National Natural Science Foundation of China(Grant Nos.12071386 and 11671330)。; In this paper,a class of holomorphic invariant metrics is introduced on the irreducible classical domains of typesⅠ-Ⅳ,which are strongly pseudoconvex complex Finsler metrics in the strict sense of Abate and Patrizio...; 关键词：holomorphic invariant metric Kahler-Berwald metric irreducible classical domains

Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds: 《Science China Mathematics》2024年第7期1665-1718,共54页Qi’an Guan Zhitong Mi Zheng Yuan; 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)。; 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 ...; 关键词：minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex K?hler manifold

Random gradient-free method for online distributed optimization with strongly pseudoconvex cost functions: 《Control Theory and Technology》2024年第1期14-24,共11页Xiaoxi Yan Cheng Li Kaihong Lu Hang Xu; supported by the National Natural Science Foundation of China(Nos.62103169,51875380);the China Postdoctoral Science Foundation(No.2021M691313).; This paper focuses on the online distributed optimization problem based on multi-agent systems. In this problem, each agent can only access its own cost function and a convex set, and can only exchange local state inf...; 关键词：Multi-agent system Online distributed optimization Pseudoconvex optimization Random gradient-free method

Zeroth-Order Methods for Online Distributed Optimization with Strongly Pseudoconvex Cost Functions: 《Journal of Systems Science and Information》2024年第1期145-160,共16页Xiaoxi YAN Muyuan MA Kaihong LU; Supported by National Natural Science Foundation of China(62103169,51875380);China Postdoctoral Science Foundation(2021M691313)。; This paper studies an online distributed optimization problem over multi-agent systems.In this problem,the goal of agents is to cooperatively minimize the sum of locally dynamic cost functions.Different from most exis...; 关键词：multi-agent systems strongly pseudoconvex function single-point gradient estimator online distributed optimization

Concavity of minimal L^(2) integrals related to multiplier ideal sheaves on weakly pseudoconvex Kahler manifolds被引量：2: 《Science China Mathematics》2022年第5期887-932,共46页Qi'an Guan Zhitong Mi; supported by National Natural Science Foundation of China (Grant Nos. 11825101, 11522101 and 11431013); 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...; 关键词：multiplier ideal sheaf plurisubharmonic function weakly pseudoconvex Kahler manifold sublevel set

FINITE TYPE CONDITIONS ON REAL HYPERSURFACES WITH ONE DEGENERATE EIGENVALUE: 《Acta Mathematica Scientia》2021年第6期1949-1958,共10页Wei CHEN Yingxiang CHEN Wanke YIN; The third author was supported in part by NSFC(12171372).; Let M be a smooth pseudoconvex hypersurface in ℂ^(n+1) whose Levi form has at most one degenerate eigenvalue. For any tangent vector field L of type (1, 0), we prove the equality of the commutator type and the Levi fo...; 关键词：pseudoconvex hypersuface finite type Levi form holomorphic vector field

REVISITING A NON-DEGENERACY PROPERTY FOR EXTREMAL MAPPINGS: 《Acta Mathematica Scientia》2021年第6期1829-1838,共10页Xiaojun HUANG; Partially supported by NSF grants DMS-1665412 and DMS-2000050.; We extend an earlier result obtained by the author in [7].; 关键词：non-degeneracy property extremal mapping PSEUDOCONVEX

L^(2) EXTENSIONS WITH SINGULAR METRICS ON K?HLER MANIFOLDS: 《Acta Mathematica Scientia》2021年第6期2021-2038,共18页Xiangyu ZHOU Langfeng ZHU; the National Natural Science Foundation of China(11688101 and 11431013);the National Natural Science Foundation of China(12022110,11201347 and 11671306).; 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...; 关键词：singular metric optimal L^(2)extension theorem strong openness of multiplier ideal sheaf generalized Siu’s lemma weakly pseudoconvex Kähler manifold

Locally Conformal Pseudo-Kahler Finsler Manifolds被引量：1: 《Chinese Quarterly Journal of Mathematics》2021年第3期244-251,共8页LI Hong-jun; Supported by the National Natural Science Foundation of China(Grant No.12001165);Postdoctoral Research Foundation of China(Grant No.2019M652513);Postdoctoral Research Foundation of Henan Province(Grant No.19030050).; In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and local...; 关键词：Strongly pseudoconvex complex Finsler metric Locally conformal pesudo-Kahler Finsler metric Kahler metric

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