Duality of Moduli and Quasiconformal Mappings in Metric Spaces

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.

Keywords

• quasiconformal mapping
• modulus of a family of surfaces
• finite perimeter
• fine topology
• poincaré inequality
• primary: 30l10
• secondary: 26b30, 31e05