On quadratic differentials on multiply connected domains that are perfect squares. II.

Problems on extremal decomposition of a multiply connected domain are considered. Two theorems exhibiting the role in such problems of quadratic differentials that are perfect squares are proved. As an implication, it is shown that the extremal metric approach used in the paper naturally leads to the results recently obtained by Dubinin and Eyrikh (Zap. Nauchn. Semin. POMI, 314, 52–75 (2004)) with the use of the capacity theory for generalized condensers. Bibliography: 2 titles. [ABSTRACT FROM AUTHOR]