位置：立项数据库 > 立项详情页
调和映射的几何
  • 项目名称：调和映射的几何
  • 项目类别：重点项目
  • 批准号：10531090
  • 申请代码：A0103
  • 项目来源：国家自然科学基金
  • 研究期限：2006-01-01-2009-12-31
  • 项目负责人：彭家贵
  • 负责人职称：教授
  • 依托单位：中国科学院大学
  • 批准年度：2005
中文摘要：

研究子流形的法度、曲率与复结构，解决了DDVV猜想；利用调和映射理论研究复Grassmann流形和复射影空间中的极小球面的几何，研究它的分类和几何量，如Gauss曲率、Kaehler角以及它的度、法曲率等等；研究Hamiltonian极小Lagrangian子流形构造、r-极小子流形变分问题及其稳定性、具有常数r+1-次异项平均曲率超曲面变分问题等；研究高余维数极小子流形Bernstein定理和平均曲率流，Grassman流形上凸函数，作出了高余维数时的Schoen-Simon-Yau型曲率估计以及Ecker-Huisken型的曲率估计，研究Finsler几何中的比较定理。研究伪欧氏空间中的具有平行平均曲率的类空子流形的Bernstein定理，引入不定special Lagrangian 子流形，推广了Harvey-Lawson，Joyce等的结果，研究不定special Lagrangian 子流形的存在性和显式构造。显式地构造了一类从平面到2维双曲空间的光滑的blow-up的Schrodinger映照，对于离散的Heisenberg方程，揭示了它在传递问题中具有量子混沌现象。

中文主题词： 调和映射；子流形几何；Lagrangian子流形；平均曲率流；Schrodinger映照。
结论摘要：

英文主题词Harmonic maps; geometry of submanifolds; Lagrangian submanifolds; mean curvature flows; Schrodinger maps.

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
  • 44
  • 0
  • 0
  • 0
  • 0
期刊论文
On surfaces immersed in Euclidean space R~4 Dedicated to Professor Yang Lo on the Occasion of his 70
Chern-Simons Invariant and Conformal Embedding of a 3-Manifold
FINITENESS OF HIGHER CODIMENSIONAL DISJOINT MINIMAL GRAPHS
On differential equations describing 3-dimensional hyperbolic spaces
Curvature and integrability of an almost Hermitian structure
Classification of Lagrangian Willmore submanifolds of the nearly Kaehler 6-sphere S-6(1) with consta
Embedded rotational hypersurfaces with constant scalar curvature in S-n: a correction to a statement
Ricci curvature and fundamental group
Bernstein type theorems with flat normal bundle
Anisotropic version of a theorem of H. Hopf
SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A SPHERE
Compact Embedded Hypersurfaces with Constant Higher Order Anisotropic Mean Curvatures
Curvature estimates for minimal submanifolds of higher codimension
THE MOBIUS CHARACTERIZATIONS OF WILLMORE TORI AND VERONESE SUBMANIFOLDS IN THE UNIT SPHERE
An inequality between Willmore functional and Weyl functional for submanifolds in space forms
Lagrangian spheres in the 2-dimensional complex space forms
A new variational characterization of the Wulff shape
Stability of area-preserving variations in space forms
Integral formula of Minkowski type and new characterization of the Wulff shape
Some explicit examples of Hamiltonian minimal Lagrangian submanifolds in complex space forms
Classification of Mobius isoparametric hypersurfaces in S-5
A variational problem for submanifolds in a sphere
r-Minimal submanifolds in space forms
Minimal 2-spheres in a complex projective space
Bott generator and its application to an almost complex structure on S-6
Global poincare inequalities on the Heisenberg group and applications
Comparison theorems in Finsler geometry and their applications
Compact embedded rotation hypersurfaces of Sn+1
Convex functions on Grassmannian manifolds and Lawson-Osserman problem
Mean curvature flow with convex Gauss image
Pseudo-holomorphic curves of constant curvature in complex Grassmannians
Chaotic properties between the nonintegrable discrete nonlinear Schrodinger equation and a nonintegr
从S^2到CP^n的共形极小浸入
Bernstein theorems for space-like graphs with parallel mean curvature and controlled growth
从S~2到CP~n的共形极小浸入(英文)
Holomorphic two-spheres in complex Grassmann manifold G(2,4)
A proof of the DDVV conjecture and its equality case
AN INTEGRAL FORMULA AND ITS APPLICATION TO NORMAL EULER NUMBER
Hamiltonian-minimal Lagrangian submanifolds in Kaehler manifolds with symmetries
相关项目
高维Klein群的组合定理及其应用
期刊论文 9
芬斯拉空间的调和映射的存在性和热流
期刊论文 10 著作 2
关于Klein群与拟共形映射相关性质的研究
期刊论文 36
Kahler流形中几类子流形的几何与分析
期刊论文 8
几何中非线性方程紧性与奇点的研究
期刊论文 6 会议论文 1
整体微分几何、曲率与拓扑不变量
期刊论文 27 著作 2
整体微分几何的若干问题
期刊论文 17 会议论文 3 著作 2
Kahler流形及子流形的几何
期刊论文 11
数学
期刊论文 6 会议论文 3
彭家贵的项目
对称空间中的极小球面的几何
Kahler流形及子流形的几何
期刊论文 11