Geometry & Topology

Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk

David Epstein and Vladimir Markovic

Full-text: Open access

Abstract

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.

Article information

Source
Geom. Topol., Volume 11, Number 1 (2007), 517-595.

Dates
Received: 28 September 2006
Accepted: 14 February 2007
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513799839

Digital Object Identifier
doi:10.2140/gt.2007.11.517

Mathematical Reviews number (MathSciNet)
MR2302497

Zentralblatt MATH identifier
1154.30012

Subjects
Primary: 30C62: Quasiconformal mappings in the plane 37E10: Maps of the circle 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces
Secondary: 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensions

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

Citation

Epstein, David; Markovic, Vladimir. Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk. Geom. Topol. 11 (2007), no. 1, 517--595. doi:10.2140/gt.2007.11.517. https://projecteuclid.org/euclid.gt/1513799839


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