Geometric Complex Analysis

几何复分析

基本信息

批准号：
09304014
负责人：
NOGUCHI Junjiro
金额：
$ 15.87万
依托单位：
University of Tokyo (1998-2000)Tokyo Institute of Technology (1997)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (A).
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09304014/
关键词：
several complex variables geometric complex analysis Kobayahsi hyperbolic manifold value distribution invariant metric moduli space pseudoconvex domain Teichmuller space モジュライ理論タイヒミューラー理論

项目摘要

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.

在价值分布理论中，为几个变量的函数字段建立了Nevanlinna-Cartan理论，从而得出有限定理作为应用。就半阿伯里亚品种而言，第二个主要定理由野口，Yamanoi，Winkelmann证明，他们还表明，整个曲线的分布类似于积分点的分布，并获得了其维度估计值。关于全态映射的Uniqeness定理，Shirosaki的Aihara，Fujimoto Aihara获得了一些结果。 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由Kamimoto Komatsu获得。 ohsawa证明了新的分歧，l^2延伸定理，以及在p^2中，实际分析性的levi-flat hyperface的不存在，尤其是复杂的谎言基团的功能理论特性，尤其是复杂的quasi-tori，尤其是复杂的quasi-tori，由卡萨马，abe，abe，umeno，umeno and th the th phimorphicize andse and Shimize and Somidiids and Shimiziend and Somidiid andiz andiiz的形式所产生的结果。通过Kodama的边界，纳卡诺（Nakano）在弱1元中的歧视中的猜想是由他本人和安倍（Abe）和安倍（Abe）的lefschetz定理解决的。由Mabuchi，Bando-Calabi-Futaki特征被证明是对半稳定性的阻碍。 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.本研究项目由Noguchi指导。