Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk

Epstein, David; Markovic, Vladimir

doi:10.2140/gt.2007.11.517

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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

Volume 11, issue 1 (2007)