Quasimöbius invariance of uniform domains
Volume 261 / 2021
Studia Mathematica 261 (2021), 1-24
MSC: Primary 30C65, 30L10, 30F45; Secondary 30C20.
DOI: 10.4064/sm191215-22-10
Published online: 26 April 2021
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, $\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.
