[1]郭辉,冯小高,崔泽建.基于角域对数导数意义下区域的单叶性内径[J].深圳大学学报理工版,2008,25(4):437-440.
 GUO Hui,FENG Xiao-gao,and CUI Ze-jian.The inner radius of univalence in the sense of pre-Schwarzian derivative based on angular domain[J].Journal of Shenzhen University Science and Engineering,2008,25(4):437-440.
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基于角域对数导数意义下区域的单叶性内径()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第25卷
期数:
2008年4期
页码:
437-440
栏目:
数学与应用数学
出版日期:
2008-10-31

文章信息/Info

Title:
The inner radius of univalence in the sense of pre-Schwarzian derivative based on angular domain
文章编号:
1000-2618(2008)04-0437-04
作者:
郭辉1冯小高12崔泽建2
1)深圳大学数学与计算科学学院,深圳518060
2)西华师范大学数学与信息学院,南充637002
Author(s):
GUO Hui1FENG Xiao-gao12and CUI Ze-jian2
1)College of Mathematics and Computable Science,Shenzhen University,Shenzhen 518060,P. R. China
2)College of Mathematics & Information,China West Normal University,Nanchong 637002,P. R. China
关键词:
万有Teichmüller空间对数导数单叶性内径拟共形反射Poincarè度量
Keywords:
universal Teichmüller spacepre-Schwarzian derivativeinner radius of univalencequasiconformal reflection
分类号:
O 174.55;O 174.51
文献标志码:
A
摘要:
研究对数导数意义下区域的单叶性内径. 以角域为基础,给出对数导数意义下区域的单叶性内径下界的两个公式.借助Becker和Pommerenke给出的在右半平面的非单叶函数,获得对数导数意义下区域的单叶性内径上界估计.最后给出关于椭圆的拟共形反射.
Abstract:
The inner radius of univalence of domains in the sense of pre-Schwarzian derivative was studied. Two general formulas for the lower bound of inner radius in the sense of pre-Schwarzian derivative based on angular domain were established. By means of one holomorphic non-univalent function given by Becker and Pommerenke,one formula for the upper bound of the inner radius was obtained. The quasiconformal reflection for the ellipse was given at the end.

参考文献/References:

[1]Nehari J. 希瓦尔兹导数与单叶函数[J]. 美国布尔数学学会会刊,1949,55:545-551(英文版).
[2]Ahlfors L V. 拟共形扩张的充分条件[J]. 数学年刊,1974,79:23-29(英文版).
[3]Becker J. 洛纳方程与拟共形映射[J]. J Reine Angew数学,1972,255:23-43(德文版).
[4]Becker J,Pommerenke Ch. 单叶性内径与约当曲线[J]. J Reine Angew数学,1984,354:74-94(德文版).
[5]Zhuravlev I V. 万有Teichüller空间模型[J]. 西伯利亚数学杂志,1986,27:75-82(英文版).
[6]陈纪修,魏寒柏. 万有Teichüller空间模型的几何性质[J].数学年刊(中国),1997,18B(3):309-314(英文版).
[7]程涛,陈纪修. 区域对数导数单叶性内径[J]. 中国科学,2007,37(4):504-512.


[1]Nehari Z. The schwarzian derivative and schlicht function[J]. Bull Amer Math Soc,1949,55:545-551.
[2]Ahlfors L V. Sufficient condition for quasiconformal exten-sion[J]. Ann of Math Studies,1974,79:23-29.
[3]Becker J. Loewner equation and qusiconformal mapping[J]. J Reine Angew Math,1972,255:23-43(in German).
[4]Becker J,Pommerenker Ch. The inner radius of univalence and Jordan curve[J]. J Reine Angew Math,1984,354:74-94 (in German).
[5]Zhuravlev I V. Model of the universal Teichmüller space[J]. Sib Math J,1986,27:75-82.
[6]CHEN Ji-xiu,WEI Han-bai. Some geometric properties on a model of universal Teichmüller space[J]. Chinese Annals of Mathetmatics,1997,18B(3):309-314.
[7]CHENG Tao,CHEN Ji-xiu,On the inner radius of univalence by pre-Schwarzian derivative[J]. Science of China,2007,37(4):504-512(in Chinese).

备注/Memo

备注/Memo:
收稿日期:2008-03-28;修回日期:2008-06-06
基金项目:国家自然科学基金资助项目(10371078);广东省自然科学基金资助项目(04009797)
作者简介:郭辉(1966-),男(汉族),四川省安岳县人,深圳大学教授、博士.E-mail:hguo@szu.edu.cn
更新日期/Last Update: 2008-11-26