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 language | English |
---|---|
Pages (from-to) | 1-24 |
Number of pages | 24 |
Journal | Studia Mathematica |
Volume | 261 |
Issue number | 1 |
DOIs | |
State | Published - 2021 |
Keywords
- (relative) quasimöbius mapping
- Min-max property
- Natural condition
- Quasisymmetric mapping
- Uniform domain