Estimates for Quasiconformal Mappings onto Canonical Domains

Vo Dang Thao

Keywords: k-quasikonformal mappings, Riemann moduli of a multiply-connected domain, monotony of the modulus of a double-connected domain In this paper we establish estimates for $K$-quasiconformal mappings $z = g(w)$ of a domain bounded by two circles $|w| = 1, |w| = q$ and $n$ continua situated in $q < |w| < 1$ onto a circular ring $Q (g) < |z| < 1$ that has been slit along $n$ arcs on the circles $|z| = R_j(g) \ \ (j = 1,\ldots,n)$ such that $|z| = 1$ and $|z| = Q$ correspond to $|w| = 1$ and $|w| = q$, respectively. The bounds in the estimates for $Q$, $R_j$ and $|g(w)|$ are explicitly given, most of them are optimal. They are deduced mainly from [17].

Classification (MSC2000): 30C62, 30C75, 30C80, 30C30

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