Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 4, pp. 819825 (1999) 

Estimates for Quasiconformal Mappings onto Canonical DomainsVo Dang ThaoUniversity of Ho Chi Minh City, Department of Mathematics, 227 Nguyen Van Cu, Q 5, Ho Chi Minh City, Vietnam, thaovd@usa.netKeywords: kquasikonformal mappings, Riemann moduli of a multiplyconnected domain, monotony of the modulus of a doubleconnected 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 Full text of the article:
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