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Semisolidity and locally weak quasisymmetry of homeomorphisms in metric spaces

Volume 242 / 2018

Manzi Huang, Antti Rasila, Xiantao Wang, Qingshan Zhou Studia Mathematica 242 (2018), 267-301 MSC: Primary 30C65; Secondary 30C20. DOI: 10.4064/sm8629-6-2017 Published online: 8 February 2018

Abstract

We investigate the relationship between semisolidity and locally weak quasisymmetry of homeomorphisms in quasiconvex and complete metric spaces. We generalize the main result of Huang and Liu (2015) and give a complete solution to an open problem given there. Two applications are given.

Authors

  • Manzi HuangDepartment of Mathematics
    Hunan Normal University
    Changsha, Hunan 410081, People’s Republic of China
    and
    School of Mathematical Science
    Qufu Normal University
    Qufu, Shandong 273165, People’s Republic of China
    e-mail
  • Antti RasilaDepartment of Mathematics and
    Systems Analysis
    Aalto University
    FI-00076 Aalto, Finland
    e-mail
  • Xiantao WangDepartment of Mathematics
    Shantou University
    Shantou 515063, People’s Republic of China
    e-mail
  • Qingshan ZhouDepartment of Mathematics
    Shantou University
    Shantou 515063, People’s Republic of China
    e-mail
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