Approximation of quasiconformal mappings by SG circle patterns

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.

Keywords:

• Beltrami equation
• quasiconformal mapping
• conformal welding
• SG circle pattern

AMS Subject Classifications:

• 65N10
• 65N30
• 52C15
• 30G62

Notes

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