# Conformal welding and Koebe’s theorem

### Abstract

It is well known that not every orientation-preserving homeomorphism of the circle to itself is a conformal welding, but in this paper we prove several results which state that every homeomorphism is “almost” a welding in a precise way. The proofs are based on Koebe’s circle domain theorem. We also give a new proof of the well known fact that quasisymmetric maps are conformal weldings.

## Authors

Christopher J. Bishop

Department of Mathematics
SUNY Stony Brook
Stony Brook, NY 11794
United States