Geometric Complex Analysis

点击翻译按钮获取中文摘要

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.