Duality of moduli and quasiconformal mappings in metric spaces

2019/05/08 by Rebekah Jones, Jones, Rebekah, Panu Lahti +1
Mathematics · #26B30 #30L10 #31E05 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:26B30 #msc:30L10 #msc:31E05

paper · pdf · doi:10.48550/arxiv.1905.02873

arxiv created 2019/05/08 · arxiv updated 2019/05/09

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.

Related

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• Quasiconformal curves and quasiconformal maps in metric spaces
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• On the Sharp Lower Bound for Duality of Modulus
• Reciprocal lower bound on modulus of curve families in metric surfaces