Gromov双曲Holder区域的边界性质  

Boundary Properties of Gromov Hyperbolic Holder Domains

作　　者：周青山 李浏兰[2] 李希宁 SAMINATHAN PONNUSAMY Qing Shan ZHOU;Liu Lan LI;Xi Ning LI;Saminathan PONNUSAMY(School of Mathematics and Big Data,Foshan University,Foshan 528000,P.R.China;College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421001,P.R.China;Department of Mathematics,Sun Yat-sen University,Guangzhou 510275,P.R.China;Department of Mathematics,Indian Institute of Technology Madras,Chennai 600036,India Department of Mathematics,Petrozavodsk State University,Lenina 33,185910 Petrozavodsk,Russia)

机构地区：[1]佛山科学技术学院数学与大数据学院,佛山528000 [2]衡阳师范学院,衡阳421001 [3]中山大学数学系,珠海510970 [4]Indian Institute of Technology Madras India 600036 [5]Department of Mathematics,Petrozavodsk State University,Lenina 33,185910 Petrozavodsk,Russia

出　　处：《数学学报（中文版）》2023年第4期651-662,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11901090,12071121);粤港澳智能微纳光电技术联合实验室(2020B1212030010);广东省教育厅项目(2021KTSCX116);广东省基础与应用基础研究基金(2021A1515012289);广州市科技计划项目(2021-02-01-05-3001-0024);湖南省自然科学基金(2020JJ6038);湖南省教育厅科学研究项目(20A070);衡阳师范学院科研专项(KYZX21002)。

摘　　要：设Ω■R^(n)是一个满足拟双曲边界条件的Gromov双曲区域.通过使用直径型的Gehring-Hayman不等式和Bonk-Heinonen-Koskela的一致化过程,我们在此文中建立了Ω的内直径边界和Gromov边界的双边H?lder对应关系.作为应用,我们不仅可以得到拟共形映射的内直径边界连续性,也可以得到关于拟双曲度量的拟等距映射在内直径边界的连续性.Let Ω■R^(n)be a Gromov hyperbolic domain which satisfies a quasihyperbolic boundary condition.In this paper we prove that there is a bi-Holder identification between the internal boundary of Ω and the Gromov boundary endowed with a visual metric by using a diameter type Gehring-Hayman inequality and also the uniformization of Bonk-Heinonen-Koskela.As an application,we establish the internal boundary continuity not only for quasiconformal homeomorphisms,but also for rough quasi-isometries between the domains with respect to the quasihyperbolic metrics.

关 键 词：Holder区域 Gromov双曲区域 HOLDER连续性 拟双曲度量 

分 类 号：O177.2[理学—数学]