The module problem for families of classes of curves in a circular ring

Earlier, the author has considered the extremal metric problem for the families of several homotopic classes of curves in the closed plane $\bar{ \mathbb{C} }$ or in a simply connected domain in $\bar{ \mathbb{C} }$. In this paper, these results are extended to the case of the modulus problem for families of classes of curves in a doubly connected domain.