Geometric researches in complex analysis

复杂分析中的几何研究

• 批准号: 12304007
• 负责人: FUJIMOTO Hirotaka
• 金额: $ 16.99万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12304007/
• 关键词: hyperbolic manifold; value distribution theory; holomorphic mapping; uniqueness theorem; defect; holomorphic automorphism group; complex dynamics; complex differential equation; 一意性多項式; 双曲型多様体; 多項式自己同型写像; 正則レフシェッツ指数; 正則曲線; 一般複素楕円形; 理想境界; ヨル

The purpose of this research is to investigate complex analysis in the aspect of geometry and, moreover, to give applications of complex analysis to geometry. To these ends, we need to have interchanges of researchers in various fields of mathematics. We held various sympsiums many times and obtained many new results in these fields.H. Fujimoto succeeded in the constructions of hyperbolic hypersurfaces of degree 2^n in the n (【greater than or equal】3)-dimensional complex projective space. He also obtained some sufficient conditions for polynomials to be uniqueness polynomials. S. Mori, together with Y. Aihara, constructed many examples of holomorphic mappings into the complex projective space with pre-assinged positive deficiency. T. Ueda studied fixed points of polynomial automorphisms of C^n and showed that the sum of holomorphic Lefshetz indices vanishes for generalized Henon maps under some conditions. By introducing the notion of balayage vector potentials, H. Yamaguchi maked clear the importance of harmonic forms. H. Sato founded many kinds of Jorgensen groups. H. Kazama studied complex analytic cohomology groups of topologically trivial line bundles over 1-dimension complex torus and showed the existence of formal Hartogs-Laurent series associated with line bundles. A. Kodama investigated the conditions for domains whose boundary are strongly pseudo-convex excluding some singularities to become complete Riemannian manifolds with respect to Webster me trices.

这项研究的目的是研究几何形状方面的复杂分析，此外，将复杂分析应用于几何形状。为了这些目的，我们需要在数学的各个领域进行研究人员的交流。我们多次举行了各种四点，在这些领域中获得了许多新的结果。藤本岛在n（[大于或相等] 3）二维复杂的射弹空间中取得了2^n的双曲超曲面的构建。他还获得了多项式的一些足够条件，使其成为独特的多项式。莫里（S. T. ueda Studiod c^n多项式自态的固定点，并表明在某些条件下，全态lefshetz指数的总和消失了概括的亨逊地图。通过引入Balayage矢量电位的概念，H。Yamaguchi明确了谐波形式的重要性。 H. Sato建立了许多Jorgensen群体。哈萨马（H. A. Kodama调查了边界强烈伪convex的域的条件，不包括一些奇异性，这些奇异性是关于Webster Me Trices的完整Riemannian歧管。

项目成果

M.Shirosaki: "A family of polynomials with the uniqueness poperty for linearly nondeger be hlomoyhic mapings"Kodai Mathematical Journal. 25. 288-292 (2002)

M.Shirosaki：“具有线性非德格同调映射的唯一性的多项式族”Kodai Mathematical Journal。

Seiki Mori: "Defects of holomorphic curves into P^n(C) for rational moving targets and a space of meromorphic mappings"Complex Variables. 43. 363-379 (2001)

Seiki Mori：“有理移动目标的全纯曲线到 P^n(C) 的缺陷和亚纯映射空间”复杂变量。

Hiroki Satoh: "Jorgensen's inequality for classical Schottky groups of real type, II"Journal of Mathematical Society of Japan. 53. 791-811 (2001)

Hiroki Satoh：“实型经典肖特基群的乔根森不等式，II”日本数学会杂志。

Akio Kodama: "A remark on generalized complex ellipsoids with spherical boundary points"Korean Math. J.. 51. 285-295 (2000)

Akio Kodama：“关于具有球形边界点的广义复杂椭球体的评论”韩国数学。

Akio Kodama: "A remark on generalized complex ellipsoids with spherical boundary points"Korean Mathematical Journal. 51. 285-295 (2000)

Akio Kodama：“关于具有球形边界点的广义复杂椭球体的评论”韩国数学杂志。