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Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property

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Arkiv för Matematik

Abstract

We characterize quasiconformal mappings as those homeomorphisms between two metric measure spaces of locally bounded geometry that preserve a class of quasiminimizers. We also consider quasiconformal mappings and densities in metric spaces and give a characterization of quasiconformal mappings in terms of the uniform density property introduced by Gehring and Kelly.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Helsinki, Finland

    Riikka Korte & Niko Marola

  2. Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH, 45221-0025, U.S.A.

    Nageswari Shanmugalingam

Authors
  1. Riikka Korte
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  2. Niko Marola
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  3. Nageswari Shanmugalingam
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Corresponding author

Correspondence to Niko Marola.

Additional information

N. Shanmugalingam was supported in part by the Taft Foundation of the University of Cincinnati.

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Korte, R., Marola, N. & Shanmugalingam, N. Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. Ark Mat 50, 111–134 (2012). https://doi.org/10.1007/s11512-010-0137-x

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  • DOI: https://doi.org/10.1007/s11512-010-0137-x

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