Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk

Epstein, David¹ ; Markovic, Vladimir²

¹ Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
² Department of Mathematics, Universiy of Stony Brook, Stony Brook, NY 11794, USA

Geometry & topology, Tome 11 (2007) no. 1, pp. 517-595.

Résumé

We prove that it is not possible to extend, in a homomorphic fashion, each quasisymmetric homeomorphism of the circle to a quasiconformal homeomorphism of the disk.

Détail

DOI : 10.2140/gt.2007.11.517

Keywords: quasiconformal, quasisymmetric, circle, low-dimensional manifolds, group actions in low dimensions, quasiconformal mappings in the plane, maps of the circle, homeomorphisms and diffeomorphisms of planes and surfaces

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