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研究了卡勒流形和全纯复向量丛上的爱因斯坦度量的存在性问题，认为爱因斯坦度量的存在性和稳定性之间一定存在良好的关系，他还写出了一个有用的泛函公式。一篇论文展示了如何使用格林函数来获得调和几何对象。Nishikawa 与 Keisuke Ueno（山形大学）合作，研究了无穷远的狄利克雷问题负曲率齐次空间之间的调和映射，以及复双曲空间之间的调和映射的复解析性，C2D14D1到边界的真调和映射在边界上给出非简并CR映射，被证明是全纯的。Urakawa继续研究。调和映射、Yang-Mills 连接等，并推广了在有限或无限图上工作的方法，他获得了谱的结果。拉普拉斯算子、Gr … More een 函数的估计以及调和映射的模拟。石田研究了推广与环面簇密切相关的（有理）扇形的实扇形。他引入了关于实扇形的外代数的分级模块，并且定义了一个对偶函子。他获得了 Serre 对偶性和 Poincare 对偶性的量。Takagi 研究了 A. Gierer 和 H. Meinhardt 提出的反应扩散系统作为基本模型形态发生和弯曲泛函上的约束变分问题，给出了红细胞形状变换的模型。伊泽基研究了作用于实空间形式的克莱因群的熵刚性和凸紧性，他获得了关于不等式的猜想的部分解决。凸余紧克莱因群极限集的豪斯多夫维数和群的上同调维数。中川研究了Bando-Calabi-Futaki特征和在一定的假设下，他将 Fano 流形已知的一些性质推广到一般射影流形及其 Kahler 类，证明了单能群李代数上 Bando-Calabi-Futaki 特征的消失以及 Bando-Calabi 升力的存在性。 -Futaki 字符组字符较少。