Conformal welding and Koebe’s theorem
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.
@article{10_4007_annals_2007_166_613,
author = {Christopher J. Bishop},
title = {Conformal welding and {Koebe{\textquoteright}s} theorem},
journal = {Annals of mathematics},
pages = {613--656},
publisher = {mathdoc},
volume = {166},
number = {3},
year = {2007},
doi = {10.4007/annals.2007.166.613},
mrnumber = {2373370},
zbl = {1144.30007},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.166.613/}
}
TY - JOUR AU - Christopher J. Bishop TI - Conformal welding and Koebe’s theorem JO - Annals of mathematics PY - 2007 SP - 613 EP - 656 VL - 166 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2007.166.613/ DO - 10.4007/annals.2007.166.613 LA - en ID - 10_4007_annals_2007_166_613 ER -
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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