Conformal welding and Koebe¿s theorem

• Autores: Christopher J. Bishop
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 166, Nº 3, 2007, págs. 613-656
• Idioma: inglés
• DOI: 10.4007/annals.2007.166.613
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• Resumen

  • 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.