Geometric Complex Analysis

在值分布理论中，建立了多元函数场的Nevanlinna-Cartan理论，给出了有限定理的应用。在半交换变种的情形下，Noguchi，Yamanoi，Winkelmann证明了第二个主要定理，并证明了整条曲线的分布类似于整点的分布，并得到了它们的维数估计。关于全纯映射的唯一性定理，Aihara，Fujimoto，Shirosaki得到了一些结果。Fujimoto Shirosaki构造了双曲射影超曲面的新例子.在CR几何中，Kuranishi关于复杂结构变形的程序由Miyajima完成，Fefferman关于Bergman核在强伪凸边界附近的渐近展开的猜想由Hirachi解决，新的CR不变量由Komatsu，Kamimoto得到.Ohsawa在P^2中证明了新的除法，L^2延拓定理和实解析Levi平坦超曲面的不存在性。Kazama，Abe，Umeno在复李群，特别是复拟环面的函数论性质方面，清水在管域的全纯等价问题上得到了新的结果，Koama在椭球体的边界上刻画了椭球。Takayama解决了弱1-完备流形上的Nakano猜想，并将他和Abe应用于半交换变种的Lefschetz定理。Mabuchi指出，Bando-Calabi-Futaki特征是半稳定的障碍。Yoshikawa在解析挠率的自同构性质方面取得了一些进展，Tsuji在解析Zariski分解的应用方面取得了一些进展，在其他方面，上田、西村得到了关于复杂二项式系统的新结果，Terada、Kato得到了关于超几何函数的结果，Tomari、Okuma、Tsuji得到了关于奇点及其变形的新结果。目前的研究项目是由野口指导的。

In value distribution theory, the Nevanlinna-Cartan theory was established for function fields of several variables, which yields finitness theorems as applications. In the case of semi-abelian variety, the Second Main Theorem was proved by Noguchi, Yamanoi, Winkelmann, who also showed that the distribution of entire curves is analogous to that of integral points, and obtained their dimension estimates. On uniqeness theorem of holomorphic mappings, some results were obtained by Aihara, Fujimoto, Shirosaki. New examples of hyperbolic projective hypersurfaces were constructed by Shirosaki, Fujimoto.In CR geometry, Kuranishi's program on deformation of complex strutures was accomplished by Miyajima, Fefferman's conjecture on the asymptotic expansion of the Bergman kernel near the strongly pseudo-convex boundary was settled by Hirachi, and new CR invariants were obtained by Komatsu, Kamimoto. Ohsawa proved new divison, L^2 extension theorems, and the non-existence of real analytic Levi-flat hypersurfaces in P^2.New results on function theoretic property of complex Lie groups, especially complex quasi-tori were obtained by Kazama, Abe, Umeno, those on the holomorphic equivalence problem of tube domains by Shimizu, and those on the characterization of ellipsoids by their boundary by Kodama.Nakano's conjecture on weakly 1-complete manifolds was solved by Takayama with application by himself and Abe to the Lefschetz theorem for semi-abelian varieties. By Mabuchi, the Bando-Calabi-Futaki character was shown to be an obstruction to the semi-stability. Some progress were made by Yoshikawa on the automorphic property of analytic torsion, and by Tsuji concerning applications of analytic Zariski decompositions.About other areas, new results on complex dinamical systems were obtained by Ueda, Nishimura, those on hypergeometric functions by Terada, Kato, and those on singularities and their deformations by Tomari, Okuma, Tsuji. The present research project was directed by Noguchi.