The Schwarzian Derivative of Harmonic Mappings in the Plane  

作　　者：Liping NIE Zongxin YANG 

机构地区：[1]Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China

出　　处：《Chinese Annals of Mathematics,Series B》2020年第2期193-208,共16页数学年刊（B辑英文版）

基　　金：the National Natural Science Foundation of China(No.11261022)。

摘　　要：In this paper, the authors introduce a definition of the Schwarzian derivative of any locally univalent harmonic mapping defined on a simply connected domain in the complex plane. Using the new definition, the authors prove that any harmonic mapping f which maps the unit disk onto a convex domain has Schwarzian norm ||Sf||≤ 6. Furthermore, any locally univalent harmonic mapping f which maps the unit disk onto an arbitrary regular n-gon has Schwarzian norm||Sf||≤8/3.

关 键 词：Schwarzian DERIVATIVE Schwarzian NORM HARMONIC MAPPING 

分 类 号：O174.5[理学—数学]