Extremal Decompositions of Riemann Surfaces and Quasiconformal Mappings of Special Form. II.

Let ℜ be a finite Riemann surface. For a quadratic differential on ℜ associated with a certain problem on extremal decomposition of ℜ into n domains, a parametric family of quasiconformal mappings fΚ : ℜ → ℜΚ K = (k1,...,ks), ki ∈ C. is defined. These mappings map the domains of the extremal decomposition of ℜ onto the domains of the extremal decomposition of ℜΚ. This allows one to study the functional dependence of the problem on the parameters. Bibliography: 6 titles. [ABSTRACT FROM AUTHOR]