Abstract
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):
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(a)
Ø has a lift to the universal cover Δ which is the identity on S1;
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(b)
Ø is homotopic to the identity rel the ideal boundary of X; and
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(c)
Ø is isotopic to the identity rel ideal boundary, through uniformly quasiconformal maps.
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© 1988 Springer-Verlag New York Inc.
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Earle, C.J., McMullen, C. (1988). Quasiconformal isotopies. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_12
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DOI: https://doi.org/10.1007/978-1-4613-9602-4_12
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