Quasimöbius invariance of uniform domains

Qingshan Zhou*, Antti Rasila

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume261
Issue number1
DOIs
StatePublished - 2021

Keywords

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

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