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POLYGONAL QUASICONFORMAL MAPPINGS AND CHORD-ARC CURVES

Part of: Riemann surfaces Geometric function theory

Published online by Cambridge University Press:  02 November 2016

SHENGJIN HUO ,
SHENGJIAN WU  and
HUI GUO
SHENGJIN HUO*
Affiliation:
Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China email huoshengjin@tjpu.edu.cn
SHENGJIAN WU
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China email wusj@math.pku.edu.cn
HUI GUO
Affiliation:
College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China email hguo@szu.edu.cn
*
✉huoshengjin@tjpu.edu.cn
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Abstract

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In this paper we show that a polygonal quasiconformal mapping always corresponds to a chord-arc curve. Furthermore, we find that the set of curves corresponding to polygonal quasiconformal mappings is path connected in the set of all bounded chord-arc curves.

Keywords

chord-arc curvepolygonal quasiconformal mappingconformal welding

MSC classification

Primary: 30C62: Quasiconformal mappings in the plane
Secondary: 30C75: Extremal problems for conformal and quasiconformal mappings, other methods 30F60: Teichmüller theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 1 , February 2017 , pp. 66 - 72
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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