An Approach to Studying Quasiconformal Mappings on Generalized Grushin Planes
Complex Variables
2014-10-22 v2 Metric Geometry
Abstract
We demonstrate that the complex plane and a class of generalized Grushin planes , where is a function satisfying specific requirements, are quasisymmetrically equivalent. Then using conjugation we are able to develop an analytic definition of quasisymmetry for homeomorphisms on spaces. In the last section we show our analytic definition of quasisymmetry is consistent with earlier notions of conformal mappings on the Grushin plane. This leads to several characterizations of conformal mappings on the generalized Grushin planes.
Keywords
Cite
@article{arxiv.1406.4176,
title = {An Approach to Studying Quasiconformal Mappings on Generalized Grushin Planes},
author = {Colleen Ackermann},
journal= {arXiv preprint arXiv:1406.4176},
year = {2014}
}