[1]刘金雄.Reich的一个定理改进及其相关问题[J].华侨大学学报(自然科学版),2000,21(1):8-10.[doi:10.3969/j.issn.1000-5013.2000.01.002]
　Liu Jinxiong.Improving One of Reich’s Theorems and Problem Correlated with It[J].Journal of Huaqiao University(Natural Science),2000,21(1):8-10.[doi:10.3969/j.issn.1000-5013.2000.01.002]
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Reich的一个定理改进及其相关问题()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第21卷
期数:
2000年第1期
页码:
8-10
栏目:
出版日期:
2000-01-20

文章信息/Info

Title:
Improving One of Reich’s Theorems and Problem Correlated with It
文章编号:
1000-5013(2000)01-0008-03
作者:
刘金雄
华侨大学管理信息科学系, 泉州362011
Author(s):
Liu Jinxiong
Dept. of Manag. Info. Sci., Huaqiao Univ., 362011, Quanzhou
关键词:
拟共形映照;  唯一极值映照;  Teichmüller映照
Keywords:
quasiconformal mapping;  uniquely extremal mapping;  Teichmüeller mapping
分类号:
O174.55
DOI:
10.3969/j.issn.1000-5013.2000.01.002
摘要:
设 f为关于φ0 的 Teichmüller映照,若存在函数列 {φn} β(Ω ),使得 limn→∞ φn(z) =φ0 (z),a.e.,limn→∞ Ω[k|φn|- Re(κfφn) ]dxdy=0,其中 κf 为 f 的复特征,Reich证明 f 是唯一极值映照 .在此基础上,证明去掉 f 为 Teichmüller映照这一假设,Reich的结论仍成立 .文中还得到在一定条件下,Reich这一结论的逆命题也成立 .
Abstract:
Assuming f to be Teichmüeller mapping of φ 0 .Reich proved that f is the uniquely extremal mapping if there exist function sequence {φ n}β(Ω) to make lim n→∞φ n(z)=φ 0(z),a.e., lim n→∞Ω[k|φ n|- Re (κ fφ n)] d x d y=0, where κ f is composite character of f . On this basis, the author proves that Reich’s conclusion can be established even if f is not assumed to be Teichmüller mapping; and that the inverse proposition of Reich’s conclusion can also be established under definite condition.

参考文献/References:

[1] Reich E. A criterion for unique extremality of Teichmüller mappings [J]. Indiana University Mathematics Journal, 1981, (30):441-447.
[2] Reich E. On criteria for unique extremality of Teichmüller meppings [J]. Annales Academic Scientiarum Fennicae Mathematica, 1981(6):289-301.
[3] 刘增荣. Reich的一个定理的改进 [J]. 华侨大学学报(自然科学版), 1989(1):1-5.

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备注/Memo

备注/Memo:
福建省自然科学基金资助项目
更新日期/Last Update: 2014-03-23