On the Solutions for Grotzsch Annulus Extremal problem

Xie Zhichun, Huang Xinzhong

Abstract

Using the properties of planar quasiconformal mappings, we obtain the solutions for the Grotzsch extremal problem on the annulus. We also point out the shortcoming used in [3] for solving this extremal problem. Moreover, by the hyperbolic area distortion and the property of domain module, one criterion for the solution of the Grotzsch annulus extremal problem is given under some conditions.

Keywords

Gr\"otzsch extremal problem, quasiconformal mapping, hyperbolic area distortion

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