A note on the relationship between quasi-symmetric mappings and φ-uniform domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Wang, Xiantao¹  Zhou, Qingshan¹  Guan, Tiantian²  Huang, Manzi²  Rasila, Antti³ 

[1] Shantou Univ, Dept Math, Shantou 515063, Guangdong, Peoples R China

[2] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

[3] Aalto Univ, Dept Math & Syst Anal, POB 11100, FI-00076 Aalto, Finland

关键词: Distance ratio metric;    Quasihyperbolic metric;    Uniform domain;    phi-uniform domain;    Quasi-symmetric mapping;   

DOI  :  10.1016/j.jmaa.2016.07.049

来源: Elsevier

【 摘 要 】

The aim of this note is to construct a psi-uniform domain G in the complex plane C such that the identity mapping id: (G,(jG)) -> (G, k(G)) is not an eta-quasi-symmetric mapping for any homeomorphism eta [0, infinity) -> [0, infinity). This result shows that the answer to the related open problem, posed by Hasto, Klen, Sahoo and Vuorinen, is negative. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free