Estimates for Quasiconformal Mappings onto Canonical Domains (II)

In this paper we establish estimates for K-quasiconformal mappings z = g(w) of a domain bounded by two circles Itol = 1, 1wl = q and n continua situated in q < Iwi < 1 onto a circular ring Q(g) < IzI < 1 that has been slit along n arcs on the circles IzI = R(g) (j = 1,... ,n) such that I zi = 1 and IzI = Q correspond to Iwl = 1 and Itul = q, respectively. The bounds in the estimates for Q, R, and g(w)i are explicitly given, most of them are optimal. They are deduced mainly from [17].