Title: Discrete conformal welding

Authors: G. Brock Williams

Issue: Volume 53 (2004), Issue 3, 765-804


Classically the process of conformal welding played a key role in the development of Teichm\"uller theory and quasiconformal maps. More recently, it has gained attention from physicists as the mechanism for switching between two models of the Universal Teichm\"uller Space, which is becoming increasingly important in string theory. We develop a geometric method for constructing conformal weldings using circle packings. We consider weldings created by bilipschitz, quasisymmetric, and locally quasisymmetric identification maps and exhibit several computer-generated examples. This provides the first method for computing these weldings.