Complex Manifolds and Gauge Theory

复流形和规范理论

基本信息

批准号：
09440027
负责人：
BANDO Shigetoshi
金额：
$ 8.77万
依托单位：
TOHOKU UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1999
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09440027/
关键词：
Einstein harmonic maps Carnot groups Laplace operators on graphs toric varieties reaction-diffusion system complex Kleinian groups Futaki character 安定性グリーン関数カルノ-群

项目摘要

Bando studied the existence problems of Einstein metrics on Kahler manifolds and holomorphic complex vector bundles. It is believed that there must be good relations between the existence of Einstein metrics and stabilities. He obtained a useful formula on a functional which connects them. He also wrote a paper which shows how Green functions can be used to obtain harmonic geometric objects.Nishikawa, jointly with Keisuke Ueno (Yamagata Univ.), studied the Dirichlet problem at infinity for harmonic maps between homogeneous spaces of negative curvature, and the complex analyticity of harmonic maps between complex hyperbolic spaces. A proper harmonic map which is CィイD14ィエD1 upto boundary and gives non-degenerate CR map on the boundaries is shown to be holomorphic.Urakawa continued to study harmonic maps, Yang-Mills connections and etc., and generalized the methods to work on graphs. On finite or infinite graphs, he obtained results on the spectra of Laplace operators, the estimates on Gr … More een functions and the analog of harmonic maps.Ishida studied real fans which generalize (rational) fans which are closely related to toric varieties. He introduced a category of graded modules of exterior algebra over real fans and defined a dualizing functor. He obtained counterparts of Serre duality and Poincare duality.Takagi studied a reaction-diffusion system which is posed by A. Gierer and H. Meinhardt as a fundamental model of morphogenesis and a constrained variational problem on a bending functional which gives a model of the shape transformation of erythrocyte.Izeki studied entoropy rigidity and convex compactness of Kleinian groups acting on real space forms. He obtained a partial resolution of a conjectire on the inequality between the Hausdorff dimension of the limit sets of convex co-compact Kleinian groups and the cohomological dimension of the groups.Nakagawa studied Bando-Calabi-Futaki characters and generalized some of properties which were known to Fano manifolds to general projective manifolds and their Kahler classes. Under certain assumption, he showed a vanishing of Bando-Calabi-Futaki characters on the Lie algebra of unipotent groups and the existence of lifts of Bando-Calabi-Futaki characters to group characters. Less

Bando研究了爱因斯坦指标在Kahler歧管和全体形态复杂载体束上的存在问题。人们认为，爱因斯坦指标和条件的存在之间必须存在良好的关系。他在连接它们的功能上获得了有用的公式。他还撰写了一篇论文，该论文显示了如何使用绿色功能来获得谐波几何对象。Nishikawa，与keisuke ueno（Yamagata）Univ共同使用。一个适当的谐波图是CII D14E D1到边界，并在边界上给出了非脱位的Cr图被证明是Holomorphic.urakawa继续研究谐波图，Yang-Mills连接等，并推广了在图上工作的方法。在有限或无限的图上，他获得了拉普拉斯操作员光谱的结果，对GR的估计……更多的een函数和谐波映射的类似物。Ishida研究的真实风扇，这些风扇概括（理性）风扇与圆磨变化密切相关。他介绍了一类外部代数的分级模块，并定义了双重函数。 izeki sutodiodiode的组合刚度和凸的紧凑性的紧凑性，作用于真实空间形式。他对凸的凸界限制组的不平等范围之间的不平等措施得到了部分分辨率。在某些假设下，他在单一群体的谎言代数上显示了Bando-Calabi-Futaki角色的消失，以及Bando-Calabi-Futaki角色的升力为组人物。较少的