Gromov hyperbolicity in the free quasiworld. I
Volume 268 / 2023
Studia Mathematica 268 (2023), 23-49
MSC: Primary 30C65; Secondary 30F45, 30L10, 30C20.
DOI: 10.4064/sm210825-7-3
Published online: 18 July 2022
Abstract
With the aid of a Gromov hyperbolic characterization of uniform domains, we first give an affirmative answer to an open question arisen by Väisälä under weaker assumption. Next, we show that the three-point condition introduced by Väisälä is necessary to obtain quasisymmetry for quasimöbius maps between bounded connected spaces in a quantitative way. Based on these two results, we investigate the boundary behavior of freely quasiconformal and quasihyperbolic mappings on uniform domains of Banach spaces and partially answer another question raised by Väisälä in different ways.
