[1]李东征,陈行堤.调和映照的Landau定理[J].华侨大学学报(自然科学版),2012,33(5):584-589.[doi:10.11830/ISSN.1000-5013.2012.05.0584]
　LI Dong-zheng,CHEN Xing-di.Landau Theorem for Planar Harmonic Mappings[J].Journal of Huaqiao University(Natural Science),2012,33(5):584-589.[doi:10.11830/ISSN.1000-5013.2012.05.0584]
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第33卷
期数:
2012年第5期
页码:
584-589
栏目:
出版日期:
2012-09-20

文章信息/Info

Title:
Landau Theorem for Planar Harmonic Mappings
文章编号:
1000-5013(2012)05-0584-06
作者:
李东征;  陈行堤
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
LI Dong-zheng;  CHEN Xing-di
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和映照;  Landau定理;  Bloch常数;  单叶函数
Keywords:
Harmonic mapping;  Landau theorem;  Bloch constant;  univalent function
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.2012.05.0584
文献标志码:
A
摘要:
研究调和映照的Landau定理和单叶性半径估计问题, 结合有界单叶函数的Koebe定理和调和映照的Schwarz引理, 得到Landau常数的渐进精确表示,改进了陈怀惠等近期的研究结果.
Abstract:
In this paper, we study Landau theorem and the univalence radius for harmonic mappings in the plane. Combining Koebe theorem of bounded univalent functions and Schwarz lemma of harmonic mappings, we obtain an asymptotically sharp estimate of Landau constant for a harmonic mapping. Our results improve the ones recently gotten by H. H. Chen and P. M. Gauthier.

参考文献/References:

[1] CHEN Huai-hui,GAUTHIER P M,HENGARTNER W.Bloch constants for planar harmonic mappings[J].Proc Amer Math Soc,2000,128(11):3231-3240.
[2] AHLFORS L V.复分析[M].北京:机械工业出版社,2005.
[3] LANDAU E.Der picard-schottysche satz und die blochsche konstanten[M].Berlin:Sitzungsber Press Akad Wiss,1926:467-474.
[4] CHEN Huai-hui,GAUTHIER P M.The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings[J].Proc Amer Math Soc,2011,139(2):583-595.
[5] GRIGORYAN A.Landau and Bloch theorems for harmonic mappings[J].Complex Variable Theory Appl,2006,51(1):81-87.
[6] HUANG Xing-zhong.Estimates on Bloch constants for planar harmonic mappings[J].J Math Anal Appl,2008,337(2):880-887.
[7] COLONNA F.The Bloch constant of bounded harmonic mappings[J].Indiana Univ Math J,1989,38:829-840.
[8] DORFF M,NOWAK M.Landau’s theorem for planar harmonic mappings[J].Comput Meth Funct Theory,2004,4:151-158.
[9] LIU Ming-sheng.Landau’s theorems for biharmonic mappings[J].Complex Variables and Elliptic Equations,2008,53(9):843-855.
[10] LIU Ming Sheng.Landau’s theorem for planar harmonic mappings[J].Computers and Mathematics with Applications,2009,57(7):1142-1146.
[11] 李东征,陈行堤.调和映照的Bloch 常数[J].华侨大学学报:自然科学版,2012,33(1):103-106.
[12] DUREN P.Harmonic mappings in the plane[M].Cambridge:Cambridge Univ Press,2004.
[13] 李忠.复分析导引[M].北京:北京大学出版社,2004.
[14] CHUAQUI M.HERNANDEZ R.Univalent harmonic mappings and linearly connected domains[J].J Math Anal Appl,2007,332(2):1189-1194.
[15] 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.
[16] PICK G.Über die konforme Abbildung eines Kreises auf ein schlichtes und zugleich beschränktes Gebiet[J].S-B Kaiserl Akad Wiss Wien Math Natur Kl Abt Ⅱa,1917,126:247-263.

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备注/Memo

备注/Memo:
收稿日期: 2011-10-22
通信作者: 陈行堤(1976-),男,副教授,主要从事函数论的研究.E-mail:chxtt@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11101165); 福建省自然科学基金资助项目(2011J01011); 中央高校基本科研业务费专项基金资助项目,华侨大学基本科研专项基金资助项目(JB-ZR1136)
更新日期/Last Update: 2012-09-20