调和映照与其剪切函数的单叶性  

Univalent Relation between Harmonic Mapping and Its Shear Function

作　　者：石擎天[1] 黄心中[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》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)

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.

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 

分 类 号：O174.51[理学—数学] O174.55[理学—基础数学]