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分析学中若干前沿问题研究
  • 项目名称：分析学中若干前沿问题研究
  • 项目类别：创新研究群体科学基金
  • 批准号：10721061
  • 申请代码：A0105
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2010-12-31
  • 项目负责人：周向宇
  • 负责人职称：研究员
  • 依托单位：中国科学院数学与系统科学研究院
  • 批准年度：2007
中文摘要：

研究群体由数学所分析学骨干、多位杰出青年基金获得者组成。研究群体的研究方向主要是分析学的重要方向如复动力系统、偏微分方程、临界点理论、多复分析等，群体拟主攻的科学问题是关于流行上的几何与分析，这是现代数学的核心和主流课题之一，具有很强的交叉性和综合性。研究群体拟在现有基础上，面对数学知识爆炸之背景，采取必要措施，进一步加强彼此之间的学术交流，不同研究内容的交叉、融合，拓展对分析学自身诸多方面理论与技巧的了解与掌握，增进对分析学与其它数学分支乃至物理的深刻联系的了解，以提高对数学的整体认识和科研水平。研究工作主要集中在分析学中诸方向如复分析、实分析、偏微分方程等及其交叉研究和在其它数学分支乃至物理中的应用。研究群体瞄准分析数学及其相关领域的国际主流方向与前沿问题，按照国际一流水平的要求，奋发向上，在科学研究、队伍建设和人才培养等方面,力争作出深刻并有重大国际影响的工作，为提高我国分析学的研究水平和国际地位做出贡献。

中文主题词：
成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
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  • 1
期刊论文
Quantum deformations of Schwarzschild and Schwarzschild–de Sitter spacetimes
Some Results About Holomorphic Vector Bundles Over General Hopfmanifolds
Automorphism groups of invariant domains in the complexification of isotropy irreducible homogeneous
Infinitely many stationary solutions of discrete vector nonlinear Schr?dinger equation with symmetry
Stability to the global large solutions of 3-D Navier-Stokes equation
Quasi-neutral limit for a model of viscous plasma
Infinitely many solutions for a class of nonlinear Dirac equations without symmetry
Solutions for periodic Schrodinger equation with spectrum zero and general superlinear nonlinearitie
Holomorphic invariant forms of a bounded domain
Rigidity and regularity in group actions
Translating solutions to symplectic and Lagrangian mean curvature flows
Scalar curvature equation on Sn, Part I: Topological conditions
Poission kernel and Cauchy formula of a non-symmetric transitive domain
Non existence of quasi-harmonic spheres
Scalar curvature equation on Sn ,Part II: Analytic characterizations
Noncommutative fields and actions of twisted Poincare algebra
Global wellposedness to 3-D anisotropic Navier-Stokes system
The Navier-Stokes-Vlasov-Fokker-Planck system near equilibrium
On the topology of wandering Julia components
Distortion control of conjugacies between quadratic polynomials
Smooth rigidity at infinity of negatively curved manifolds, Preprint
Cross ratio, invariant 2-form for Anosov flows and geometric applications, Preprint
A mathematical foundation of neuroscience, Preprint
The Pseudo-affine transformations in
Application Of Symbolic Computation In Nonlineardifferential-Difference Equations
Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation
Solutions for discrete periodic Schr?dinger equations with spectrum 0
Scalar curvature equation on Sn Part II: Analytic characterizations
The Conjugate Points of and The Zeroes of Bergman Kernel
Positive mass theorems for asymptotically de Sitter spacetimes
Variational approach to various nonlinear problems in geometry and physics
Gravitational collapse of spherically symmetric stars in noncommutative general relativity
一般Hopf曲面上向量丛的结构
Symplectic critical surfaces in K?hler surfaces, 2010
Vector bundles on non-primary Hopf manifolds with abelian fundamental group
A new characterization for isometries by triangles
Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system
Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems
A note on superlinear Hamiltonian elliptic systems
On a diffusion system with bounded potential, Discrete Contin
Multiple semiclassical solutions for the nonlinear Maxwell-Schrodinger system
Solutions of a class of Hamiltonian elliptic systems in R^N
Positive mass theorems for asymptotically AdS spacetimes with arbitary cosmological constant
A new quasi-local mass and positivity
A quasi-loval mass for 2-spheres with negative Gauss curvature
On the Initial-Boundary Value Problem of the Incompressible Viscoelastic Fluid System
Remark on the Regularities of Kato's Solutions to Navier-Stokes Equations with Initial Data in Ld(Rd
On the regularity for stationary harmonic maps
Existence and multiplicity of solutions for a non-periodic Schrodinger equation
S tationary states of nonlinear Dirac equations with general prtentials
So lutions of a nonlinear Dirac equation with external fields
会议论文
On a quasi-local mass,
Deformation quantization and noncommutative black holes,
Quasi-local quantities and limits at spatial and null infinities
Some recent results in several complex variables
华罗庚对中国数学科学事业的贡献,
Renormalization and wandering continua,
Non existence of quasi-harmonic spheres
Singularities of heat flows of harmonic maps,
Quasi-local quantities and limits at spatial and null infinities
On the Scalar Curvature equations
Rigidity and regularity in group actions
Eigenvalues of the Dirac operator on manifolds with boundary and the Alexandrov theorem
Positive mass theorems for asymptotically de Sitter spacetimes, 
Einstein field equations in noncommutative spacetimes
Topological Method on the scalar curvature equation
Variational methods for strongly indefinite problems,
On the free boundary problem to 3-D visco-elastic system,
Global wellposedness to 3-D anisotropic Navier-Stokes system,
Steady states of Fokker-Planck equation
Einstein field equations in noncommutative spacetimes
Sympletic Critical surfaces
Rigidity and envelopes of holomorphy in group actions, Oberwolfach
Variational Methods for Strongly Indefinite Problems,
Positive mass theorems for asymptotically de Sitter spacetimes,
Non-existence of quasi-harmonic sphere
Sympletic Critical surfaces
Sympletic Critical surfaces
Two ways to find holomorphic curves in Kahler surfaces,
The conformal Laplacian operator and the mass of asymptotically flat manifolds,
Einstein field equations in noncommutative spacetimes
Two ways to find holomorphic curves in Kahler surfaces,
On nonlinear Dirac equations
强不定问题的变分方法,
Scalar curvature equation on Sn
Scalar Curvature Equation on Sn
Positive mass theorems for asymptotically AdS spacetimes with arbit ary cosmological constant,
Isometries in hyperbolic spaces
Global solutions to 3-D incompressible anisotropic Navier-Stokes equations in the some critical spac
Steady states of Fokker-Planck equation
On the global weak solution to 1-D Variational wave equation
著作
《中国科学》 复分析专辑, Vol.53, No.3, 客座主编, 2010
周向宇的项目
多复变与李群论
多复变函数论
《数学译林》
分析学中若干前沿问题研究
期刊论文 81 著作 4
资助“数学译林”
《数学译林》
流形上的几何、分析和计算
期刊论文 2
分析学中若干前沿问题研究
期刊论文 54 会议论文 49 著作 1
《数学译林》
多复变与复几何前沿问题研究
多复变与复几何若干问题研究
期刊论文 21 会议论文 2