Geometry and Analysis of Strongly Pseudoconvex CR Structure and Contact Structure

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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