Quasiconformal isotopies

  • Clifford J. Earle
  • Curt McMullen
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 10)


Let X be a hyperbolic Riemann surface or orbifold, possibly of infinite topological complexity. Let Ø: X → X be a quasiconformal map. We show the following conditions are equivalent (§1):
  1. (a)

    Ø has a lift to the universal cover Δ which is the identity on S1;

  2. (b)

    Ø is homotopic to the identity rel the ideal boundary of X; and

  3. (c)

    Ø is isotopic to the identity rel ideal boundary, through uniformly quasiconformal maps.



Riemann Surface Harmonic Measure Kleinian Group Fuchsian Group Ideal Boundary 
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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Clifford J. Earle
    • 1
    • 2
  • Curt McMullen
    • 2
  1. 1.Cornell UniversityIthacaUSA
  2. 2.M.S.R.I.BerkeleyUSA

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