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Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property. (English) Zbl 1278.30026

Authors’ abstract: We characterize quasiconformal mappings as those homeomorphisms between two metric 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.

MSC:

30C65 Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations
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