双曲度量和Roper-Suffridge算子  

Hyperbolic metric and Roper-Suffridge extension operator

作　　者：王建飞 刘太顺[3] 唐笑敏[3] Jianfei Wang;Taishun Liu;Xiaomin Tang

机构地区：[1]华侨大学数学科学学院,泉州362021 [2]计算科学福建省重点实验室,泉州362021 [3]湖州师范学院理学院,湖州313000

出　　处：《中国科学：数学》2022年第4期369-380,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12071161,11971165和12071130);福建省自然科学基金(批准号:2020J01073);华侨大学科研(批准号:19BS102)资助项目。

摘　　要：本文以双曲度量为工具,获得了复平面上单连通区域的若干分析性质,并且应用这些性质分别研究Roper-Suffridge算子和扰动的Roper-Suffridge算子的分析与几何特性.本文不仅给出利用双曲度量研究多复变数双全纯映照的新方法,而且所得结果更为一般和深刻.In this paper, by using the hyperbolic metric, we obtain several analytic properties of a simply connected domain in the complex plane, which can be applied to study the analytic and geometric properties on the Roper-Suffridge extension operator and its modification, respectively. This hyperbolic metric can be viewed as not only providing an alternative approach to study biholomorphic mappings in several complex variables, but also generalizing many known results deeply.

关 键 词：双全纯映照 双曲度量 Loewner链 星形映照 

分 类 号：O177[理学—数学]