Volume 11, issue 1 (2007)
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Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk

David Epstein and Vladimir Markovic
Geometry & Topology 11 (2007) 517–595
DOI: 10.2140/gt.2007.11.517
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.

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
Mathematical Subject Classification 2000
Primary: 30C62, 37E10, 37E30
Secondary: 57M50, 57M60
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Publication
Received: 28 September 2006
Accepted: 14 February 2007
Published: 16 March 2007
Proposed: Martin Bridson
Seconded: Jean-Pierre Otal, Wolfgang Lück
Authors
David Epstein
Mathematics Institute
University of Warwick
Coventry CV4 7AL
UK
Vladimir Markovic
Department of Mathematics
Universiy of Stony Brook
Stony Brook, NY 11794
USA