Quasiregular mapping by branched circle packing

Abstract

We use branched circle packings to construct an approximating sequence to a proper quasiregular mapping, that is a general proper solution of a Beltrami equation. We show that the approximating sequence converges on compact subsets, and show that for given branch-set the solution is unique subject to a certain normalization.

Keywords:

• branched circle packing
• quasiregular mapping
• Beltrami equation
• proper solution

AMS Subject Classifications:

• 52C26
• 30C62
• 30C35

Acknowledgements

This project is supported in part by NSF of China (10771220) and the Ministry of Education of China (NCET-04-0791, SRFDP-20070558043).