Geometry and Analysis of Strongly Pseudoconvex CR Structure and Contact Structure

Hisashi Naito研究了给定为Yang-Mills泛函的梯度流的流形上的非线性发展方程，并给出了一个在有限时间内爆破的解的例子；Hajime Sato研究了各种结构(例如Grassman结构)与它们的可积性条件之间的扭曲对应；Norio Ejiri研究了微分几何肖特基问题，得到了Riemann矩阵的微分几何特征；Kanai 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导数；Ryoichi Kobayashi研究了Ricci平坦Kahler度量的存在性问题和全纯曲线值分布理论中的逻辑引理。特别地，当环境空间是阿贝尔变种时，他证明了第二主要定理。芥川和夫研究了具有边界的流形和Seiberg-Witten方程的相对Yamabe不变量。Toshihiro Nakani…进一步，Shih给出了穿透面群的SL(2，C)-表示空间上的坐标系统以及映射类群在其上的作用。小谷元子研究了周期非紧流形的热核转移概率的渐近行为以及晶格上的随机游动。她还研究了负曲线流形的同调闭测地线个数的渐近行为。Shin Nayatani与Kamada Hiroyuki合作研究了CR几何的四元数模拟。他还研究了从建筑物到非正曲线空间的分段仿射映射，从而最小化了某些能量。Aiko Aiyama研究了曲面在4维欧氏空间中的浸入，证明了该映射是由由两种角度函数确定的一阶微分方程组局部给出的。大田宏志构造了Floer上同调的阻塞理论以及拉格朗日子流形的过滤A_∞-代数。Hiroyasu Izeki利用A-亏格的指标定理证明了具有正标量曲率的紧致共形平坦流形对应的Klein群是凸余紧的。Kamada Hiroyuki Kamada研究了紧复曲面上自对偶不定Kahler度量的存在性问题。他在投影线的乘积上显式地构造了一族这样的度量，并研究了如何区分它们。石破和弘研究了热方程非负解的结构。特别是，他阐明了当区域是无界的时，结构是如何受到强加条件的影响的。较少

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