Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 305-320

AN APPROACH TO STUDYING QUASICONFORMAL MAPPINGS ON GENERALIZED GRUSHIN PLANES

Colleen Ackermann

University of Illinois at Urbana-Champaign, Department of Mathematics
1409 W. Green St, Urbana, IL 61801, U.S.A.; ackrmnn2 'at' illinois.edu

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.

2010 Mathematics Subject Classification: Primary 30L10; Secondary 53C17.

Key words: Grushin plane, quasiconformal, quasisymmetric, Beltrami equation, conformal.

Reference to this article: C. Ackermann: An approach to studying quasiconformal mappings on generalized Grushin planes. Ann. Acad. Sci. Fenn. Math. 40 (2015), 305-320.

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doi:10.5186/aasfm.2015.4021