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具有线性连结像域的局部单叶调和映照 被引量：4

Locally Univalent Harmonic Mappings with Linearly Connected Image Domains
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摘要 研究了单位圆上具有像域线性连结性的局部单叶调和函数成为调和拟共形映照的充要条件,确定了一类具有线性连结像域的单叶调和函数的单叶调和稳定性参数区域,推广了Chuaqui和Hernandez的相应结果. The author studies the necessary and sufficient conditions for locally univalent harmonic mappings in the unit disk with linearly connected image domains to be harmonic quasiconformal mappings,and determines the parameter domain for a class of univalent harmonic mappings in the unit disk having the univalent harmonic stability property.The results improve and generalize the one made by Chuaqui and Hernandez.
作者 黄心中
机构地区 华侨大学数学科学学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2010年第5期625-630,共6页 Chinese Annals of Mathematics
基金 福建省自然科学基金(No.2008J0195)资助的项目
关键词 局部单叶调和函数 单叶 线性连结区域 调和拟共形映照 稳定性 Locally univalent harmonic mapping Univalent Linearly connected domain Harmonic quasiconformal mapping Stability
分类号 O174.51 [理学—基础数学]
  • 相关文献

参考文献10

  • 1Lewy H. On the non-vanishing of the Jacobian in certain one-to-one mappings [J]. Bull Amer Math Soc, 1936, 42:689-692.
  • 2Pavlovic M. Boundary correspondence under harmonic quasiconformal homeomorphisms of the unit disk [J]. Ann Acad Sci Fenn Math, 2002, 27:365-372.
  • 3Chen H H, Gauthier P M, Hengartner W. Bloch constants for planar harmonic mappings [J]. Proc Amer Math Soc, 2000, 128:3231-3240.
  • 4Dorff M, Nowak M. Landau's theorem for planar harmonic mappings [J]. Computational Methods and Function Theory, 2004, 4(1):151-158.
  • 5Grigoryan A. Landau and Bloch theorems for harmonic mappings [J]. Complex Variable Theory Appl, 2006, 51(1):81-87.
  • 6Huang X Z. Estimates on Bloch constants for planar harmonic mappings [J]. J Math Anal Appl, 2007, 337:880-887.
  • 7Liu M S. Estimates on Bloch constants for planar harmonic mappings [J]. Science in China Set A, 2008, 52(1):87-93.
  • 8黄心中.单位圆盘上的调和拟共形同胚[J].数学年刊（A辑）,2008,29(4):519-524. 被引量：11
  • 9Chuaqui M, Hernandez R. Harmonic univalent mappings and linearly connected domains [J]. J Math Anal Appl, 2007, 332:1189-1194.
  • 10Jahangiri J, Silverman H. Harmonic close-to-convex mappings [J].J Appl Math Stoch Anal, 2002, 1(15):23-28.

二级参考文献8

  • 1Choquet G., Sur une type de transformation analytique generalisant la representation conforme et definie au moyen fonctions harmoniques [J], Bull. Sci. Math., 1945, 69(2):156 165.
  • 2Lewy H., On the non-vanishing of the Jacobian in certain one-to-one mappings [J], Bull. Amer. Math. Soc., 1936, 42:689-692.
  • 3Martio O., On harmonic quasiconformal mappings [J], Ann. Acad. Sci. Fenn. Math. Ser. AI, 1968, 425:3 10.
  • 4Pavlovic M., Boundary correspondence under harmonic quasiconformal homeomorphisms of the unit disk [J], Ann. Acad. Sci. Fenn. Math., 2002, 27:365 372.
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  • 8Wang Chaoxiang and Huang Xinzhong, On the extension theorem for Zygmund functions in closed interval [J], J. Huaqiao Univ., 2006, 27:119 122.

共引文献10

同被引文献37

  • 1AHLFORS L V.复分析[M].赵志勇,薛运华,杨旭,译.北京:机械工业出版社,2005:85-113.
  • 2CHEN Huai-hui,GAUTHIER P M, HENGARTNER W. Bloch constants for planar harmonic mappings[J]. ProcAmer Math Soc?2000,128(11) :3231-3240.
  • 3LANDAU E. Der picard-schottysche satz und die blochsche konstanten[M]. Berlin: Sitzungsber Press Akad Wiss,1926:467-474.
  • 4CHEN Huai-hui, GAUTHIER P M. The Landau theorem and Bloch theorem for planar harmonic and pluriharmonicmappings[J]. Proc Amer Math Soc,2011,139(2) : 583-595.
  • 5GRIGORYAN A. Landau and Bloch theorems for harmonic mappings[J]. Complex Variable Theory Appl,2006,51(1):81-87.
  • 6HUANG Xing-zhong. Estimates on Bloch constants for planar harmonic mappings[J]. J Math Anal Appl,2008,337(2):880-887.
  • 7COLONNA F. The Bloch constant of bounded harmonic mappings[J]. Indiana Univ Math J, 1989 9 38 : 829-840.
  • 8DORFF M,NOWAK M Landau's theorem for planar harmonic mappings[J]. Comput Meth Funct Theory?2004,4;151-158.
  • 9LIU Ming-sheng. Landau's theorems for biharmonic mappings[J]. Complex Variables and Elliptic Equations, 2008,53(9):843-855.
  • 10LIU Ming Sheng. Landau's theorem for planar harmonic mappings[J]. Computers and Mathematics with Applica-tions,2009,57(7): 1142-1146.

引证文献4

二级引证文献9

数学年刊（A辑）
2010年 第5期

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