Geometry & Topology
- Geom. Topol.
- Volume 11, Number 1 (2007), 517-595.
Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk
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.
Geom. Topol., Volume 11, Number 1 (2007), 517-595.
Received: 28 September 2006
Accepted: 14 February 2007
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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
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