[1]潘旭玲,黄心中.一类单位圆盘上单叶调和映照的延拓定理[J].华侨大学学报(自然科学版),2013,34(6):701-705.[doi:10.11830/ISSN.1000-5013.2013.06.0701]
　PAN Xu-ling,HUANG Xin-zhong.Extension Theorems for Some Univalent Harmonic Mappings on the Unit Disk[J].Journal of Huaqiao University(Natural Science),2013,34(6):701-705.[doi:10.11830/ISSN.1000-5013.2013.06.0701]
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一类单位圆盘上单叶调和映照的延拓定理()
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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6期
页码:
701-705
栏目:
出版日期:
2013-11-20

文章信息/Info

Title:
Extension Theorems for Some Univalent Harmonic Mappings on the Unit Disk
文章编号:
1000-5013(2013)06-0701-05
作者:
潘旭玲; 黄心中
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
PAN Xu-ling;  HUANG Xin-zhong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
单叶调和映照;  拟共形映照;  调和拟共形延拓;  最大伸缩商
Keywords:
univalent harmonic mapping;  quasiconformal mapping;  harmonic quasiconformal extension;  maximum dilatation
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.2013.06.0701
文献标志码:
A
摘要:
研究单位圆盘D={z||z|<1}上调和映照类SHK(m,n,α,β)的调和延拓与调和拟共形延拓问题,具体给出该类映照到单位圆盘外的单叶保向调和延拓;除n=0以外,同时给出该类映照的调和拟共形延拓.作为整个平面上的拟共形映照,最后给出了最大伸缩商估计.
Abstract:
Harmonic and harmonic quasiconformal extensions for the class of univalent harmonic mappings SHK(m,n,α,β)on the unit disk are considered. The concrete sense-preserving univalent harmonic extensions and, except for n=0, the harmonic quasiconformal extensions are given. As the quasiconformal mappings in the plane, their maximum dilatations are also estimated.

参考文献/References:

[1] AHLFORS L.Lectures on quasiconformal mappings[M].Providence: American Mathematical Society,2006.
[2] AHLFORS L,WEILL G.A uniqueness theorem for Beeltrami equations[J].Proc Amer Math Soc,1962,13(6):975-978.
[3] 杨宗信,陈纪修.Nehari函数族的偏差定理与拟共形延拓[J].数学年刊,2004,25(6):695-704.
[4] 谢志春,黄心中.一类Nehari函数族的拟共形延拓与系数偏差[J].华侨大学学报:自然科学报,2011,32(3):343-347.
[5] REICH E.On extremal quasiconformal extensions of conformal mappings[J].Israel J Math,1977,28(1/2):91-97.
[6] CLUNIE J,SHELL-SMALL T.Harmonic univalent functions[J].Ann Acad Sci Fenn Ser A I Math,1984(9):3-25.
[7] SEKER B.Salagean-type harmonic univalent functions[J].International Journal of the physical Sciences,2011,6(4):801-807.
[8] PAVLOVIC M.Boundary correspondence under harmonic quasiconformal homeomorphisms of the uint disk[J].Ann Acad Sci Fenn Math,2002,27(2):365-372.
[9] KALAJ D.Quasiconformal harmonic functions between convex domains[J].Publications De L’Institut Mathematique,2004,76(90):3-20.
[10] 黄心中.单位圆上的调和拟共形同胚[J].数学年刊:A辑,2008,29(4):519-524.

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备注/Memo

备注/Memo:
收稿日期: 2012-09-29
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: 2013-11-20