Quasiconformal mappings on the Grushin plane
Metric Geometry
2021-12-20 v2
Abstract
We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal. As the main step in our argument, we show that a quasisymmetric parametrization of the Grushin plane by the Euclidean plane must also be geometrically quasiconformal. We also discuss some aspects of the Euclidean theory of quasiconformal maps, such as absolute continuity on almost every compact curve, not satisfied in the Grushin case.
Keywords
Cite
@article{arxiv.1604.02161,
title = {Quasiconformal mappings on the Grushin plane},
author = {Chris Gartland and Derek Jung and Matthew Romney},
journal= {arXiv preprint arXiv:1604.02161},
year = {2021}
}
Comments
13 pages, 1 figure, this version has additional section on conformal mappings, also minor corrections and improvements