Quasiconformal homogeneity after Gehring and Palks
Abstract
In a very influential paper Gehring and Palka introduced the notions of quasiconformally homogeneous and uniformly quasiconformally homogeneous subsets of Euclidean space. Their motivation was to provide a characterization of quasi-disks, i.e. domains which are quasiconformally homeomorphic to the unit disk. As a generalization, Bonfert-Taylor, Canary, Martin and Taylor initiated the study of uniformly quasiconformally homogeneous hyperbolic manifolds. In this paper, we review the theory of quasiconformally homogeneous subsets of Euclidean and uniformly quasiconformally homogeneous hyperbolic manifolds. We finish with a discussion of open problems in the theory.
Keywords
Cite
@article{arxiv.1401.3662,
title = {Quasiconformal homogeneity after Gehring and Palks},
author = {Petra Bonfert-Taylor and Richard Canary and Edward Taylor},
journal= {arXiv preprint arXiv:1401.3662},
year = {2014}
}
Comments
To be published in a volume of Computational Methods and Function Theory dedicated to the memory of Fred Gehring