Geometric properties of extremal decompositions and estimates for the modulus of families of curves in an annulus

We study the geometric properties of the boundary for problems on extremal decomposition into two domains of an annulus or a rectangle with a barrier removed. Sharp estimates of moduli are proved for certain families of curves bending around the barrier in a canonical domain. Bibliography: 17 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 93–114. Translated by A. Yu. Solynin.