Quasisymmetry and solidity of quasiconformal maps in metric spaces
Volume 272 / 2023
Studia Mathematica 272 (2023), 199-219
MSC: Primary 30C65.
DOI: 10.4064/sm221211-30-5
Published online: 30 August 2023
Abstract
This paper is devoted to the study of the broad problem of deriving global metric properties from local quasiconformality in metric spaces. In particular, we show that, under certain regularity and connectivity conditions, a quasiconformal map between metric spaces is weakly $(L,M)$-quasisymmetric. Furthermore, such a map is solid if the metric spaces are complete. These extend and generalize some well known results in Euclidean as well as metric spaces.
