Geometry and Analysis of Strongly Pseudoconvex CR Structure and Contact Structure

强赝凸CR结构和接触结构的几何与分析

基本信息

批准号：
11440019
负责人：
NAITO Hisashi
金额：
$ 7.23万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B).
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

项目摘要

Hisashi Naito studied the nonlinear evolution equation on a manifold given as the gradient flow for the Yang-Mills functional, and gave an example of a solution which blows up in finite time.Hajime Sato studied the twistor correspondence between various structures(e.g. Grassmannian structure)and their integrability conditions.Norio Ejiri studied the differential-geometric Schottky problem to obtain a differential-geometric characterization of Riemann matrices.Masahiko Kanai proved that the standard conformal action of the fundamental group of a closed hyperbolic manifold has local rigidity.Ryoichi Kobayashi studied the existence problem for Ricci-flat Kahler metrics and the lemma on logarithmic derivative in the value distribution theory for holomorphic curves. In particular, he proved the second main theorem when the ambient space is an Abelian variety.Kazuo Akutagawa studied the relative Yamabe invariant of a manifold with boundary as well as Seiberg-Witten equations.Toshihiro Nakani … More shi gave a coodinate system on the space of SL(2, C)-representations of a punctured-surface group and the action of the mapping class group on it.Motoko Kotani investigated the asymptotic behavior(as time goes to infinity)of the transition probability of the heat kernel of a periodic noncompact manifold as well as the random walk on a crystal lattice. She also stdudied the asymptotic behavior of the number of homologous closed geodesics of a negatively-curved manifold.Shin Nayatani studied the quaternionic analogue of CR geometry in collaboration with Hiroyuki Kamada. He also investigated piecewise affine maps from a building into a nonpositively-curved space which minimize certain energy.Reiko Aiyama studied an immerion of a surface into 4-dimensional Euclidean space, and showed that the map is locally given by the system of first order differential equations determined by two kinds of angle functions.Hiroshi ohta constructed the obstruction theory for the Floer cohomology as well as a filtered A_∞-algebra for a Lagrangian submanifold. He also clarified the existence of a contact structure which is tight but not fillable.Hiroyasu Izeki proved that the Kleinian group corresponding to a compact conformally flat manifold with positive scalar curvature is convex-cocompact by using the index theorem for the A-genus.Hiroyuki Kamada investigated the existence question for self-dual, indefinite Kahler metrics on compact complex surfaces. He explicitly constructed a family of such metrics on the product of projective lines and studied how to distinguish them.Kazuhiro Ishige studied the structure of nonnegative solutions of heat equations. In particular, he clarified how the structure is influenced by the imposed conditions when the domain is unbounded. Less

Hisashi Naito研究了联排别墅的多种梯度flow的非线性方程，并在有限的时间内给出了afterame。 STUDIED THOTTKY PROBLEM TO OBTAMETRIC ATION OF RIEMANN MATRICES.MASAHIKO KANAI PROVED THAT THE FUNDAMENTAL GROUP OF A CloseD Hyperbolic Manifold Has Local DITY.RYOICHI KOBAYASHI STUDIED THE EXISTENCE FOR RICCI-FLAT KAHLERER METRICS AND THE LEMMA ON LOGARITHMIC DERIVATIVE IN THE VALUE DISTRIBUTION THEORY FOROMORPHIC.特别是，他证明了环境空间是一个阿贝利亚品种。卡佐川（Kazuo akutagawa）研究了与边界的相对yamabe不变的歧管。 c）刺穿的表面群和映射木块在其上的作用。MotokoKotani研究了渐近行为D以及在晶格上的随机行走。弯曲的。 Hiroshi Ohta构建了for for for Flomology的阻塞，并过滤了Lagrangian Submanifold的A_∞-代数。提前剂的前毛发事件剂 - forem forem forem forem forem forem forem forem forem forem -genus.hiroyuki kamada kamada研究了自我单位的存在，在生产线上构建了这样的指标家族，并研究了如何区分负面尤其是热量方程的解决方案。