A study on the holomorphic mappings on the unit ball

单位球上的全纯映射研究

• 批准号: 14540195
• 负责人: HAMADA Hidetaka
• 金额: $ 0.58万
• 依托单位: Kyushu Sangyo University (2003-2004)Kyushu Kyoritsu University (2002)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540195/
• 关键词: holomorphic mapping; biholomorphic mapping; quasiconformal; quasiconformal extension; proper holomorphic mapping; rational mapping; 単葉写像; バナッハ空間; 螺旋型写像; 星型写像

1.We give a sufficient condition that the first element of a Loewner chain on the Euclidean unit ball can be extended to a quasiconformal homeomorphism of C^n onto itself.2.We give sufficient conditions for locally biholomorphic mappings on the unit ball in a complex Banach space to be starlike of certain order or strongly starllke.3.We obtain sufficient conditions for biholomorphic mappings on the unit ball of a complex Banach space to have parametric representation.4.We consider the generalization of the Loewner differential equation to reflexive complex Banach spaces. We obtain some Lipechitz continuity results related to Loewner chains and their transition mappings.5.We give a sharp lower bound for the distortion of the image of the Roper-Suffridge extension operator : This result gives a positive answer to an open problem posed by Liczberski-Starkov.6.We give a complete classification of rational proper holomorphic maps from B^n into B^<2n> when n>3.7.Pescar investigated the univalence of certain integral operators. We show that the results are obtained by the Schwarz lemma. We also give some generalizations.8.Let f(z,t) be a subordination chain on[0,α] on the Euclidean unit ball B in C^n. We give a sufficient condition that f can be extended to a quasiconformal homeomorphism of R^<2n> onto itself.9.We give coefficient conditions for some rational mappings to be starlike or convex on the Euclidean unit ball B in C^n.

1.给出了欧氏单位球上Loewner链的第一个元素可扩张为C^的拟共形同胚的一个充分条件2.给出了复Banach空间中单位球上的局部双全纯映射为某阶星形或强星形的充分条件; 3.给出了复Banach空间中单位球上的双全纯映射为某阶星形或强星形的充分条件4.将Loewner微分方程推广到自反复Banach空间。5.给出了Roper-Suffridge扩张算子的象的畸变的一个精确下界，这个结果肯定地回答了Liczberski-Starkov提出的一个公开问题6.当n&gt; 3时，给出了从B^n到B^n的有理真全纯映射的一个完全分类<2n>.我们证明了这些结果是由施瓦茨引理得到的。8.设f（z，t）是C^n中欧氏单位球B上[0，α]上的从属链。我们给出了f可以扩展为R^到其自身的拟共形同胚的充分条件<2n>。9.我们给出了C^n中欧几里得单位球B上某些有理映射是星形或凸的系数条件。

项目成果

Rational proper holomorphic maps from Bn into B2n

• DOI: 10.1007/s00208-004-0606-2
• 发表时间: 2005-01
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: H. Hamada

Roper-Suffridge extension operator and the lower bound for the distortion

• DOI: 10.1016/j.jmaa.2004.06.052
• 发表时间: 2004-12
• 期刊: Journal of Mathematical Analysis and Applications
• 影响因子: 1.3
• 作者: H. Hamada;G. Kohr

Quasiconformal extension of biholomorphic mappings in several complex variables

多个复变量中双全纯映射的拟共形扩展

• 发表时间: 2005
• 期刊: Journal d' Analyse Mathematique 96
• 作者: H.Hamada;G.Kohr
• 通讯作者: G.Kohr

H.Hamada, G.Kohr: "Loewner chains and quasiconformal extension of holomorphic mappings"Ann.Polon.Math.. (to appear).

H.Hamada、G.Kohr：“Loewner 链和全纯映射的拟共形扩展”Ann.Polon.Math..（即将出现）。

Loewner chains and the Loewner differential equation in reflexive complex Banach spaces

自反复数 Banach 空间中的 Loewner 链和 Loewner 微分方程

• 发表时间: 2004
• 期刊: Rev.Roumaine Math.Pures Appl. 49
• 作者: H.Hamada;G.Kohr
• 通讯作者: G.Kohr