调和映射的可积拟共形延拓  

INTEGRABLE QUASICONFORMAL EXTENSION OF HARMONIC MAPPINGS

作　　者：唐树安 冯小高[2] TANG Shu-an;FENG Xiao-gao(School of Mathematic Science,Guizhou Normal University,Guiyang 550001,China;College of Mathematics and Information,China West Normal University,Nanchong 637002,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550001 [2]西华师范大学数学与信息学院,四川南充637002

出　　处：《数学杂志》2020年第5期593-599,共7页Journal of Mathematics

基　　金：国家自然科学基金资助(11701459,11601100);西华师范大学博士启动基金(17E088);贵州省科技厅基金资助([2017]7337,[2017]5726);四川省教育厅基金(17ZB0431).

摘　　要：本文研究了平面调和映射的可积拟共形延拓问题.利用经典的共形映射的拟共形延拓方法和调和映射的性质,获得了一些条件使得调和映射可以拟共形延拓至整个平面且其复伸缩商关于双曲度量是p次可积的,推广了解析单叶函数的相关结果.In this paper,we study the integrable quasiconformal extension of harmonic mappings in the plane.By using the classical method of quasiconformal extension of conformal mapping and some properties of harmonic mappings,we obtain some conditions to ensure the harmonic mapping can be quasiconformally extended to the whole complex plane so that its complex dilatation is p integrable with respect to the hyperbolic metric.These results generalize the related results of univalent analytic functions.

关 键 词：调和映射 拟共形延拓 Pre-Schwarzaian导数 Schwarzaian导数 

分 类 号：O175[理学—数学]