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arXiv · 1905.02873

Duality of moduli and quasiconformal mappings in metric spaces

Rebekah Jones·Panu Lahti
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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 Poincar\'e 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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Rebekah Jones, Panu Lahti. 2019-05-08. Duality of moduli and quasiconformal mappings in metric spaces. https://arxiv.org/abs/1905.02873

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