Geometry and Analysis of Strongly Pseudoconvex CR Structure and Contact Structure

Hisashi Naito研究了作为Yang-Mills泛函的梯度流的流形上的非线性发展方程，并给出了一个解在有限时间内爆破的例子。Hajime Sato研究了各种结构之间的扭量对应（如Grassmannian结构）及其可积性条件。Norio Ejiri研究了微分几何Schottky问题，得到了一个微分几何Schottky问题，Riemann矩阵的几何特征。Masahiko Kanai证明了闭双曲流形的基本群的标准共形作用具有局部刚性。Ryoichi小林研究了Ricci-平坦Kahler度量和全纯曲线值分布理论中的对数导数引理。特别是，他证明了第二个主要定理时，周围的空间是一个阿贝尔品种。芥川一夫研究了相对Yamabe不变量的流形与边界以及Seiberg-Witten方程。 ...更多信息 Shi等人给出了一个关于穿孔曲面群的SL（2，C）-表示空间的坐标系以及映射类群在其上的作用. MotokoKotani研究了周期非紧流形热核的转移概率的渐近性态以及晶格上的随机游动.她还研究了负弯曲流形的同调闭测地线的数量的渐近行为。Shin Nayatani与Hiroyuki Kamada合作研究了CR几何的四元数模拟。他还研究了分段仿射地图从一个建筑物到一个nonpositively-curved空间，最大限度地减少某些能源。Hiroshi Ohta建立了Floer上同调的阻塞理论，并证明了该映射是由两类角函数所决定的一阶微分方程组局部给出的，同时也构造了一个滤A_∞-拉格朗日子流形的代数他还澄清了存在的接触结构，这是紧张的，但不fillable。Hiroyasu Izeki证明了克莱因集团对应的一个紧凑的共形平坦流形与积极的标量曲率是凸cocompact的指数定理的A-genus。Hiroyuki Kamada调查存在问题的自我对偶，不定卡勒度量紧凑复杂的表面。他明确地建造了一个家庭的这种度量的产品的投影线，并研究如何区分它们。石重和弘研究了结构的非负解的热方程。特别是，他澄清了结构是如何受到施加条件的影响时，域是无界的。少

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