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调和映照与其剪切函数的单叶性 被引量：5

Univalent Relation between Harmonic Mapping and Its Shear Function
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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 map-pings, the univalence of harmonic mappingfa（z）=h（z）＋ag（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 quasicordormal mappings is obtained.
作者 石擎天 黄心中
机构地区 华侨大学数学科学学院
出处 《华侨大学学报（自然科学版）》 CAS 北大核心 2013年第3期334-338,共5页 Journal of Huaqiao University(Natural Science)
基金 福建省自然科学基金资助项目(2011J0101)
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 univalent harmonic mapping linearly connected domain shear function harmonic quasiconformal mapping
分类号 O174.51 [理学—基础数学] O174.55 [理学—基础数学]
  • 相关文献

参考文献11

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二级参考文献14

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共引文献5

同被引文献45

  • 1LEWY H. On the non-vanishing of the Jacobian in certain one-to-one mappings [J]. Uspekhi Mat Nauk, 1948,3 (2) : 216-219.
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  • 4BSHOUTY D, LYZZAIK A. Problems and conjectures in planar harmonic mappings[J]. J Analysis, 2010,18,69-81.
  • 5HUANG Xin-zhong. Harmonic quasiconformal mappings on the upper half-plane[J]. Complex Variables and Elliptic Equations, 2013,58(7) .. 1005-1011.
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  • 9BSHOUTY D,LYZZAIK A. Close-to-convexity criteria for planar harmonic mappings[J]. Complex Analysis and Operator Theory, 2011,5(3) : 767-774.
  • 10MOCANU P T. Injeetivity conditions in the complex plane[J]. Complex Anal Oper Theory, 2011,5 (3) :759-766.

引证文献5

二级引证文献4

华侨大学学报（自然科学版）
2013年 第3期

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