Extremal functions for modules of systems of measures

We extend a result by Rodin, which provides an explicit method for finding the extremal function and the 2-module of a foliated family of curves in R 2 , to R n making use of Fuglede’s p -module of systems of measures. The extremal functions are identified and the p -module of systems of measures is computed in condensers of rather general type and in their images under homeomorphisms of certain regularity. At the beginning, we discuss and apply Rodin’s Theorem in order to obtain estimates for the conformal modules of parallelograms and ring domains in terms of directional dilatations.