Quasimöbius invariance of uniform domains

Qingshan Zhou, Antti Rasila Studia Mathematica MSC: Primary 30C65, 30L10, 30F45; Secondary 30C20. DOI: 10.4064/sm191215-22-10 Opublikowany online: 26 April 2021


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, $\delta $-uniformity and the min-max property. Then we show that all of these conditions are equivalent if the domain is $\psi $-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.


  • Qingshan ZhouSchool of Mathematics and Big Data
    Foshan University
    Foshan, Guangdong 528000
    People’s Republic of China
  • Antti RasilaMathematics with Computer Science Program
    Guangdong Technion – Israel Institute of Technology
    241 Daxue Road
    Shantou, Guangdong 515063
    People’s Republic of China
    Department of Mathematics
    Technion – Israel Institute of Technology
    Haifa 32000, Israel

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