[1]刘金雄.唯一极值映照为正则Teichmǖller映照的充要条件[J].华侨大学学报(自然科学版),2001,22(2):133-136.[doi:10.3969/j.issn.1000-5013.2001.02.005]
　Lin Jinxiong.Necessary and Sufficient Condition for the Uniquely Extremal Quasiconformal Mapping to be Regular Teichmuller Mapping[J].Journal of Huaqiao University(Natural Science),2001,22(2):133-136.[doi:10.3969/j.issn.1000-5013.2001.02.005]
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唯一极值映照为正则Teichmǖller映照的充要条件()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第22卷
期数:
2001年第2期
页码:
133-136
栏目:
出版日期:
2001-04-20

文章信息/Info

Title:
Necessary and Sufficient Condition for the Uniquely Extremal Quasiconformal Mapping to be Regular Teichmuller Mapping
文章编号:
1000-5013(2001)02-0133-04
作者:
刘金雄
华侨大学经济管理学院, 泉州362011
Author(s):
Lin Jinxiong
College of Econ. Manag., Huaqiao Univ., 362011, Quanzhou
关键词:
极值拟共形映照;  Teichmüller映照;  本质边界点;  边界特征
Keywords:
extremal quasiconformal mapping;  Teichmüller mapping;  substantial boundary point;  boundary dilatation
分类号:
O174.55
DOI:
10.3969/j.issn.1000-5013.2001.02.005
摘要:
设 f为单位圆 D={ |z|<1}到自身,且与 f有相同边界值的拟共形映照类 Qf 中的唯一极值拟共形映照,f 的最大特征 K>1.那么,f 为正则 Teichmüller映照的一个充分必要条件是存在一列 Jordan曲线 γn.γn 的内部为 Dn,∪∞n=1Gn=D,且 f|γn无本质边界点,n=1,2,… .即 γn 上的每一点关于 f|γn的点特征,都小于从 Gn 到 f( Gn)以 f|γn为边界值的极值拟共形映照的最大特征 .
Abstract:
Let f with maximal dilalation K >1, be uniquely extremal in the class Q f, where Q f denotes a class of quasiconformal mappings from unit circle D={|z |<1} to itself and with the same boundary values as f . Then, f will be regular Teichmüller mapping if and only if, there exists a sequence of Jordan curves γ n with ∪∞ n=1 G n=D,and with the property that f| γ n has no substantial boundary point for every n .

参考文献/References:

[1] Reich E. On the relation between local and global properties of boundary values for extremal quasiconformal mappings [J]. Annals of Mathematical Studies, 1974.391-407.
[2] Strebel K. On the existence of extremal Teichmüller mappings [J]. Journal of d’Analyse Mathematique, 1976.464-480.
[3] Fehlman R, Sakan K I. On the set of substantial boundary poinrs for extremal quasiconformal mappings [J]. Complex Variables, 1986.323-335.
[4] Harrington A, Ortel M. The dilataion of an extremal quasiconformal mappings [J]. Duke Mathematical Journal, 1976.533-544.doi:10.1215/S0012-7094-76-04343-X.
[5] Reich E. On criteria for unique extremality of Teichmüller mappings [J]. Annales Academic Scientiarum Fennicae Mathematica, 1981.289-302.
[6] 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(1):8-10.doi:10.3969/j.issn.1000-5013.2000.01.002.

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更新日期/Last Update: 2014-03-23