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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 4, 2002, pp. 1043–1054
DOI: 10.4171/ZAA/1125

Published online: 2002-12-31

Estimates for Quasiconformal Mappings onto Canonical Domains (II)

Vo Dang Thao[1]

(1) National University, Hochiminh City, Vietnam

In this paper we establish estimates for normal K-quasiconformal mappings $z = g(w)$ of any finitely-connected domain in the extended $w$-plane onto the interior or exterior of the unit circle or the extended $z$-plane with $n (≥ 0)$ slits on the circles $|z| = R_j (j = 1,...,n)$. The bounds in the estimates for $R_j, |g(w)|$, etc. are explicitly given. They are sharp or asymptotically sharp and deduced mainly from estimates for the inverse mappings of $g$ in our previous paper [10] based on Carleman’s and Gr¨otzsch’s inequalities and partly improved here. A generalization of the Schwarz lemma and improvements of some classical inequalities for conformal mappings are shown.

Keywords: $K$-quasiconformal mappings, Riemann moduli of a multiply-connected domain

Thao Vo Dang: Estimates for Quasiconformal Mappings onto Canonical Domains (II). Z. Anal. Anwend. 21 (2002), 1043-1054. doi: 10.4171/ZAA/1125