Arkiv för Matematik

  • Ark. Mat.
  • Volume 50, Number 1 (2012), 111-134.

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

Riikka Korte, Niko Marola, and Nageswari Shanmugalingam

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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.

Note

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

Article information

Source
Ark. Mat., Volume 50, Number 1 (2012), 111-134.

Dates
Received: 15 January 2010
Revised: 23 August 2010
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485907157

Digital Object Identifier
doi:10.1007/s11512-010-0137-x

Mathematical Reviews number (MathSciNet)
MR2890347

Zentralblatt MATH identifier
1278.30026

Rights
2011 © Institut Mittag-Leffler

Citation

Korte, Riikka; Marola, Niko; Shanmugalingam, Nageswari. Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. Ark. Mat. 50 (2012), no. 1, 111--134. doi:10.1007/s11512-010-0137-x. https://projecteuclid.org/euclid.afm/1485907157


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