关于实轴自同胚的延拓  

On Extensions of Self-homeomorphism of the Real Line

作　　者：戴译贤 钟裕民 DAI Yixian;ZHONG Yumin(School of Science,Beijing University of Posts and Telecommunications,Beijing,100876,P.R.China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《数学进展》2024年第4期707-719,共13页Advances in Mathematics（China）

基　　金：partially supported by NSFC (No.12071047);partially supported by NSFC (Nos.12071047,11701039);Fundamental Research Funds for the Central Universities (No.500421126)。

摘　　要：逐点伸缩偏差满足一定条件时,实轴保向自同胚可以由Beurling-Ahlfors扩张连续延拓为David映射.利用修改的三角剖分扩张,本文给出实轴保向自同胚连续延拓为David映射的另一个充分条件,该条件去掉了保向自同胚的一个限制.A sense-preserving self-homeomorphism of the real line can be continuously extended to a David mapping by Beurling-Ahlfors extension if the scale-wise distortion satisfies some conditions.By using a modified triangulation extension,another sufficient condition,for which a sense-preserving self-homeomorphism of the real line can be continuously extended to a David mapping,is given.This result removes one restriction on the sense-preserving selfhomeomorphism.

关 键 词：拟共形映射 拟对称 自同胚 伸缩商 Carleson盒子延拓 

分 类 号：O174.5[理学—数学]