AN APPROACH TO STUDYING QUASICONFORMAL MAPPINGS ON GENERALIZED GRUSHIN PLANES

被引：5

作者：

Ackermann, Colleen ^{[1
]}

机构：

[1] Univ Illinois, Dept Math, Urbana, IL 61801 USA

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2015年 / 40卷 / 01期

关键词：

Grushin plane; quasiconformal; quasisymmetric; Beltrami equation; conformal;

D O I：

10.5186/aasfm.2015.4021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：305 / 320

页数：16

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