A study on the structure of complex ellipsoids

复杂椭球结构的研究

• 批准号: 12640162
• 负责人: KODAMA Akio
• 金额: $ 1.98万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640162/
• 关键词: bounded domain; automorphism group; complex ellipsoid; spherical boundary point; hyperbolic hypersurface; tube domain; equivalence problem; 双正則同値; スタイン多様体; CR同値

The main purpose of this research is to solve the following fundamental con jecture : "Let D be a bounded domain in an n-dimensional complex Euclidean space C^n with non-compact automorphism group Aut(D). Then D is necessarily biholomorphic to some complex ellipsoidal domain E". Concerning this research, we studied and obtained the following :1. Kodama studied the structure of the set consisting of all non-unbilical points of a given complex ellipsoid E, and he applied his ideas to the characteri zation of complex ellipsoids with spherical boundary points.2. Fujimoto studied Nevanlinna theory of holomorphic mappings into the complex projective spaces P^nc, and obtained some new results on hyperbolic hypersurfaces in P^3c of degree 8.3. Shimizu studied the Lie algebra of polynomial vector fields on a tube domain T_Ω in C^n. He obtained Prolongation Theorem for such vector fields and solved the equivalence problem for tube domains.

这项研究的主要目的是解决以下基本猜想：“设 D 是 n 维复欧几里得空间 C^n 中具有非紧自同构群 Aut(D) 的有界域。则 D 必然是双全纯的一些复杂的椭球体域E”。关于这项研究，我们研究并获得了以下结果：1.Kodama研究了由给定复杂椭球体的所有非unbilical点组成的集合的结构E，并将其思想应用于具有球形边界点的复杂椭球体的表征。 2．Fujimoto研究了复杂射影空间P^nc的全纯映射Nevanlinna理论，并得到了关于P^3c的双曲超曲面的一些新结果。 8.3 级 Shimizu 研究了 C^n 中管域 T_Ω 上多项式向量场的李代数，他获得了此类向量场的延长定理。并解决了管域的等价问题。

项目成果

Atsushi Kasue: "Convergence of Riemanian manifolds and Laplace operators, I"Ann. Institut Fourier. 52(未定). (2002)

Atsushi Kasue：“黎曼流形和拉普拉斯算子的收敛，I”Ann。52（TBD）。

Takashi Ichinose and Hideo Tamura: "The norm convergence of the Trotter-kato product formula with error bound"Commun.Math.Phys.. (未定).

Takashi Ichinose 和 Hideo Tamura：“具有误差界的 Trotter-kato 乘积公式的范数收敛性”Commun.Math.Phys..（待定）。

Satoru Shimizu: "A classification of two-dimensional tube domains"Amer. J. Math.. 122. 1289-1308 (2000)

Satoru Shimizu：“二维管域的分类”Amer。

Junjiro Noguchi: "The second main theorem for holomorphic curves into semi-Abelian varieties"Acta Math.. 188(未定). (2002)

Junjiro Noguchi：“半阿贝尔簇全纯曲线的第二个主要定理”Acta Math.. 188（TBD）（2002）。

Kazuya Hayasida: "On some improperly posed problem for a degenerate nonlinear parabolic equation"Z.Anal.Anwendung.. 19. 395-413 (2000)

Kazuya Hayasida：“关于退化非线性抛物型方程的一些不正确提出的问题”Z.Anal.Anwendung.. 19. 395-413 (2000)