Geodesic
Conformal welding and Koebe’s theorem
Christopher J. Bishop1
1Department of Mathematics<br/>SUNY Stony Brook<br/>Stony Brook, NY 11794<br/>United States
Annals of mathematics, Tome 166 (2007) no. 3, pp. 613-656
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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.

DOI : 10.4007/annals.2007.166.613

Christopher J. Bishop  1

1 Department of Mathematics<br/>SUNY Stony Brook<br/>Stony Brook, NY 11794<br/>United States 
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Christopher J. Bishop. Conformal welding and Koebe’s theorem. Annals of mathematics, Tome 166 (2007) no. 3, pp. 613-656. doi: 10.4007/annals.2007.166.613

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