A study on the univalent mappings in several complex variables

多个复变量的单价映射研究

• 批准号: 11640194
• 负责人: HAMADA Hidetaka
• 金额: $ 0.45万
• 依托单位: Kyushu Kyoritsu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640194/
• 关键词: holomorphic mappings; biholomorphic mappings; spirallike mappings; starlike mappings; quasiconformal; balanced domain; Banach space; convex mapping

1. We considered a theory of partial differential subordinations on the unit ball in infinite dimensional complex Banach spaces and gave some applications.2. We investigated the growth of normalized spirallike mappings on the Euclidean unit ball in C^n.3. We gave a characterization of normalized spirallike mappings on bounded balanced pseudo-convex domains using subordination chains and showed the growth theorem. Moreover, we obtained a quasiconformal extension of a quasiconformal strongly spirallike mapping.4. We studied linear invariant families on the unit polydisc.5. We showed a sharp growth theorem for normalized starlike mappings of order α on the unit ball in complex Banach spaces.6. We gave an analytic sufficient condition for locally diffeomorphism on the unit ball with respect to an arbitrary norm on C^n to be univalent.7. We gave an analytic characterization for locally biholomorphic mappings on the unit ball in infinite dimensional complex Banach spaces to be biholomorphic. We also give an analytic characterization for locally biholomorphic mappings on the unit ball in complex Hilbert spaces to be a convex mapping.

1.研究了无穷维复Banach空间中单位球上的偏微分从属理论，并给出了一些应用.研究了Cn中欧氏单位球上正规螺形映射的增长性。利用从属链给出了有界平衡伪凸域上正规螺形映射的一个刻画，并证明了其增长定理。此外，我们还得到了拟共形强螺状映射的拟共形扩张.研究了单位多圆盘上的线性不变族.证明了复Banach空间中单位球上α阶正规星形映射的一个锐增长定理.给出了单位球上关于C^n上任意范数的局部同态是单叶的一个解析充分条件.给出了无穷维复Banach空间中单位球上的局部双全纯映射为双全纯映射的一个解析刻划。给出了复Hilbert空间中单位球上的局部双全纯映射为凸映射的一个解析刻划。

项目成果

H.Hamada,G.Kohr and P.Liczberski: "General partial differential subordinations for holomorphic mappings in complex Banach spaces"Demonstratio Mathematica. 33. 481-487 (2000)

H.Hamada、G.Kohr 和 P.Liczberski：“复杂 Banach 空间中全纯映射的一般偏微分从属关系”Demonstratio Mathematica。

H.Hamada and G.Kohr: "The growth of spirallike mappings."Proceedings of the second ISAAC congress. Vol.1. 231-236 (2000)

H.Hamada 和 G.Kohr：“螺旋映射的增长”。第二届 ISAAC 大会记录。

H.Hamada and G.Kohr: "The growth theorem and quasiconformal extension of strongly spirallike mappings of type α"Complex Variables. (to appear).

H. Hamada 和 G. Kohr：“α 型强螺旋映射的增长定理和拟共形扩展”复变量（即将出现）。

H.Hamada and G.Kohr: "Φ-like and convex mappings in infinite dimensional spaces."Rev.Roumaine Math.Pures Appl.. (to appear).

H.Hamada 和 G.Kohr：“无限维空间中的类 Φ 和凸映射。”Rev.Roumaine Math.Pures Appl..（即将出现）。

H.Hamada and G.Kohr: "Linear invariant families on the unit polydisc"Mathematica (Cluj). (to appear).

H.Hamada 和 G.Kohr：“单位多圆盘上的线性不变族”Mathematica（克卢日）。