调和映射的两点偏差性质  

Two-point Distortion Theorems For Harmonic Mappings

作　　者：黄翠[1] 辜承亮 

机构地区：[1]江西师范大学数学与信息科学学院,南昌332200

出　　处：《江西科学》2015年第2期148-150,172,共4页Jiangxi Science

基　　金：国家自然科学基金(11261022)

摘　　要：根据共形度量定义的Schwarz导数和Ahlfors关于曲线的Schwarz导数的定义,结合新的共形因子λ（z）=√｜h＇（z）｜^2＋｜g＇（z）｜^2）来讨论调和映射f的Weierstrass-Enneper提升f~的单叶性条件和f~在单位圆内的两点偏差定理的定量形式。In this paper we obtain a general criterion in terms of the Schwarzian derivative for global univalence of the Weierstrass-Enneper lift of a planar harmonic mapping and turn out that the harmonic lift f~ satisfies a two-point distortion condition. The analysis depends on a generalized Schwarzian defined for eonformal metrics and on a Schwarzian introduced by Ahlfors for curves.

关 键 词：调和映射 SCHWARZ导数 单叶 偏差 

分 类 号：O174.51[理学—数学]