Duality of moduli in regular metric spaces

Abstract

F. Gehring and W. Ziemer proved that the p-modulus of the family of paths connecting two continua is dual to the p^*-modulus of the corresponding family of separating hypersurfaces. In this paper we show that a similar result holds in complete Ahlfors-regular metric spaces that support a weak 1-Poincaré inequality. As an application we obtain a new characterization for quasiconformal mappings between such spaces.