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Applicable Analysis
An International Journal
Volume 93, 2014 - Issue 11: Functional theoretic methods, wavelets and applied PDEs on the occasion of Professor Wei Lin’s 80th Birthday and the 30th anniversary of Robert Gilbert visiting China. Guest editors Daoqing Dai, Yuqiu Zhao and Yongzhi Steve Xu
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Articles

Approximation of quasiconformal mappings by SG circle patterns

Hui-Ya HuSchool of Science, Guangxi University for Nationalities, Nanning530006, P. R. China.
&
Shi-Yi LanSchool of Science, Guangxi University for Nationalities, Nanning530006, P. R. China.Correspondence[email protected]
Pages 2360-2369 | Received 24 Mar 2014, Accepted 14 Aug 2014, Published online: 09 Sep 2014
 
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Abstract

Given a measurable function with , the approximating solutions of Beltrami equation for are directly constructed by using the techniques of SG circle pattern and conformal welding. It is proved that the sequence of approximating solutions converges uniformly on to compact subsets to a quasiconformal mapping with complex dilation . This provides a new approach of constructing discrete quasiconformal mappings.

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Notes

This work is supported in part by NSF of China [11161004] and NSF of Guangxi [2013GXNSFAA019015].

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