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BY 4.0 license Open Access Published by De Gruyter Open Access August 24, 2020

Duality of Moduli and Quasiconformal Mappings in Metric Spaces

  • Rebekah Jones EMAIL logo and Panu Lahti

Abstract

We prove a duality relation for the moduli of the family of curves connecting two sets and the family of surfaces separating the sets, in the setting of a complete metric space equipped with a doubling measure and supporting a Poincaré inequality. Then we apply this to show that quasiconformal mappings can be characterized by the fact that they quasi-preserve the modulus of certain families of surfaces.

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Received: 2019-03-06
Accepted: 2020-06-05
Published Online: 2020-08-24

© 2020 Rebekah Jones et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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