Computational Methods and Function Theory 2 (2002), No. 1, 281--291
Copyright Heldermann Verlag 2002
Caren N. Genthner
genthner@analysis.mathematik.uni-wuerzburg.de, Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany.
Stephan Ruscheweyh
ruscheweyh@mathematik.uni-wuerzburg.de, Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany.
Luis Salinas
lsalinas@inf.utfsm.cl, Departamento de Informática, Universidad Técnica F. Santa María, Valparaíso, Chile.
We give a non-standard criterion for closed plane curves to be quasi-simple, i.e.\ to be the boundary of a simply connected domain in $\mathbb{C}$. This can be used, for instance, to introduce piecewise close-to-convex functions and to establish the univalence of the extremal polynomials in the maximal range problem for simply connected domains.
Keywords: simple curves, univalent functions, piecewise close-to-convex.
MSC 2000: Primary 30C10; Secondary 30C55.
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