[1]石擎天,黄心中.调和映照与其剪切函数的单叶性[J].华侨大学学报(自然科学版),2013,34(3):334-338.[doi:10.11830/ISSN.1000-5013.2013.03.0334]
　SHI Qing-tian,HUANG Xin-zhong.Univalent Relation between Harmonic Mapping and Its Shear Function[J].Journal of Huaqiao University(Natural Science),2013,34(3):334-338.[doi:10.11830/ISSN.1000-5013.2013.03.0334]
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调和映照与其剪切函数的单叶性()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第3期
页码:
334-338
栏目:
出版日期:
2013-05-20

文章信息/Info

Title:
Univalent Relation between Harmonic Mapping and Its Shear Function
文章编号:
1000-5013(2013)03-0334-05
作者:
石擎天;  黄心中
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
SHI Qing-tian;  HUANG Xin-zhong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
单叶调和映照;  线性连结区域;  剪切函数;  调和拟共形映照
Keywords:
univalent harmonic mapping;  linearly connected domain;  shear function;  harmonic quasiconformal mapping
分类号:
O174.51;O174.55
DOI:
10.11830/ISSN.1000-5013.2013.03.0334
文献标志码:
A
摘要:
利用调和映照像区域的线性连结性与单叶性之间的内在联系, 研究单位圆盘D上调和映照fα(z)=h(z)+αg(z)^-与其剪切函数Fβ(z)=h(z)+βg(z)的单叶性问题.研究得到判别单位圆盘上一类局部单叶调和映照为调和拟共形映照的充分必要条件,推广了由S.L.Chen等得到的相应结果.
Abstract:
By the use of the inner relations between linear connectivity of image domains and univalence of harmonic mappings, the univalence of harmonic mapping fα(z)=h(z)+αg(z)^- and its shear function Fβ(z)=h(z)+βg(z)in the unit disk is investigated. Our results improve and generalize the one made by S.L.Chen and other authors. As an application, one necessary and sufficient condition for a class of locally univalent harmonic mappings in the unit disk to be harmonic quasiconformal mappings is obtained.

参考文献/References:

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[6] HUANG Xin-zhong.Harmonic quasiconformal mappings on the upper half-plane[EB/OL].[2012-4-27] .http://www.tandfonline.com/doi/abs/10.1080/17476933.2011.620097.
[7] 胡春英,黄心中.单叶调和函数及其反函数为拟共形映照的充要条件[J].华侨大学学报:自然科学版,2010,31(5):586-589.
[8] CLUNIE J,SHEIL-SMALL T.Harmonic univalent functions[J].Ann Acad Sci Fenn(A),1984,9(1):3-25.
[9] 黄心中.具有线性连结像域的局部单叶调和映照[J].数学年刊,2010,31A(5):625-630.
[10] CHUAQUI M,HERNAANDEZ R.Harmonic univalent mappings and linearly connected domains[J].J Math Anal Appl,2007,33(2):1189-1194.
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备注/Memo

备注/Memo:
收稿日期: 2012-04-27
通信作者: 黄心中(1957-),男,教授,主要从事函数论的研究.E-mail:huangxz@hqu.edu.cn.
基金项目: 福建省自然科学基金资助项目(2011J0101)
更新日期/Last Update: 2013-05-20