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Duality of moduli and quasiconformal mappings in metric spaces (1905.02873v1)
Published 8 May 2019 in math.MG
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.