Quasimöbius invariance of uniform domains

Qingshan Zhou*, Antti Rasila

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We study quasimöbius invariance of uniform domains in Banach spaces. We first investigate implications of certain geometric properties of domains in Banach spaces, such as (diameter) uniformity, δ-uniformity and the min-max property. Then we show that all of these conditions are equivalent if the domain is ψ-natural. As applications, we partially answer an open question proposed by Väisälä, and provide a new method to prove a recent result of Huang et al. (2013), which also gives an answer to another question raised by Väisälä.

Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalStudia Mathematica
Issue number1
StatePublished - 2021


  • (relative) quasimöbius mapping
  • Min-max property
  • Natural condition
  • Quasisymmetric mapping
  • Uniform domain


Dive into the research topics of 'Quasimöbius invariance of uniform domains'. Together they form a unique fingerprint.

Cite this