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Mathematics > Complex Variables

arXiv:1406.4176 (math)
[Submitted on 16 Jun 2014 (v1), last revised 20 Oct 2014 (this version, v2)]

Title:An Approach to Studying Quasiconformal Mappings on Generalized Grushin Planes

Authors:Colleen Ackermann
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Abstract:We demonstrate that the complex plane and a class of generalized Grushin planes $G_r$, where $r$ 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 $G_r$ 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.
Subjects: Complex Variables (math.CV); Metric Geometry (math.MG)
MSC classes: 30L10, 53C17
Cite as: arXiv:1406.4176 [math.CV]
  (or arXiv:1406.4176v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1406.4176

Submission history

From: Colleen Ackermann [view email]
[v1] Mon, 16 Jun 2014 21:29:43 UTC (12 KB)
[v2] Mon, 20 Oct 2014 23:58:35 UTC (16 KB)
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