Riemann mapping theorems for Beltrami equations by circle packings

Shi-Yi Lan and Dao-Qing Dai

Vol. 217 (2004), No. 1, 139–147

DOI: 10.2140/pjm.2004.217.139

Abstract

We use circle packing techniques to construct approximate solutions to the generalized Beltrami equations with simply and multiply connected regions in the plane. We show convergence of the approximate solutions. This gives a constructive proof for the existence of quasiconformal mappings with a given pair of complex dilations.

Milestones

Received: 15 December 2003

Revised: 20 February 2004

Published: 1 November 2004