Duality of Moduli in Regular Metric Spaces

Gehring [3] and Ziemer [17] 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-Poincare inequality. As an application, we obtain a new characterization for quasiconformal mappings between such spaces.