[1]胡春英,黄心中.单叶调和函数及其反函数为调和拟共形的充要条件[J].华侨大学学报(自然科学版),2010,31(5):586-589.[doi:10.11830/ISSN.1000-5013.2010.05.0586]
　HU Chun-ying,HUANG Xin-zhong.Necessary and Sufficient Condition that Univalent Harmonic Functions and Their Inverse Functions are Harmonic Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),2010,31(5):586-589.[doi:10.11830/ISSN.1000-5013.2010.05.0586]
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单叶调和函数及其反函数为调和拟共形的充要条件()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第31卷
期数:
2010年第5期
页码:
586-589
栏目:
出版日期:
2010-09-20

文章信息/Info

Title:
Necessary and Sufficient Condition that Univalent Harmonic Functions and Their Inverse Functions are Harmonic Quasiconformal Mappings
文章编号:
1000-5013(2010)05-0586-04
作者:
胡春英; 黄心中
华侨大学数学科学学院
Author(s):
HU Chun-ying;  HUANG Xin-zhong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
单叶调和函数;  拟共形映照;  复特征;  调和拟共形映照
Keywords:
univalent harmonic functions;  quasiconformal mappings;  complex dilatation;  harmonic quasiconformal mappings
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.2010.05.0586
文献标志码:
A
摘要:
研究平面上具有形式f(z)=A[αz+β+log(1-exp(-αz-β))-log(1-exp(-αz-β))]+B的保向单叶调和映照,其中A,B,α,β是常数且满足条件A≠0,α≠0.给出了定义在椭圆和上半平面上的单叶调和函数及其反函数都是调和拟共形映照的充要条件,并推广到一般的单连通区域上.
Abstract:
Plannar sense-preserving univalent harmonic functions with the form f(z)=A[αz+β+log(1-exp(-αz-β))-log(1-exp(-αz-β))]+B,are considered,where A,B,α,β are constants with the condition A≠0,α≠0.Necessary and sufficient condition for such harmonic functions defined elliptic domain or on the upper half plane and their inverse functions to be harmonic quasiconformal mappings are obtained.Our methods also can be applied to the general simply connect domains.

参考文献/References:

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[2] 张兆功, 刘礼泉. 单叶调和映照的反函数 [J]. 数学进展, 1996(3):270-276.
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备注/Memo

备注/Memo:
福建省自然科学基金资助项目(2008J0195); 华侨大学科研基金资助项目(09HZR23)
更新日期/Last Update: 2014-03-23