201. Harmonic mappings onto stars
- Author
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Jane McDougall, Peter Duren, and Lisbeth Schaubroeck
- Subjects
Mathematics::Complex Variables ,Blaschke product ,Applied Mathematics ,Mathematical analysis ,Harmonic (mathematics) ,Convex polygon ,Unit disk ,Dilatation ,Domain (mathematical analysis) ,symbols.namesake ,Unit circle ,Harmonic mappings ,Polygon ,Piecewise ,symbols ,Analysis ,Mathematics - Abstract
A general version of the Rado–Kneser–Choquet theorem implies that a piecewise constant sense-preserving mapping of the unit circle onto the vertices of a convex polygon extends to a univalent harmonic mapping of the unit disk onto the polygonal domain. This paper discusses similarly generated harmonic mappings of the disk onto nonconvex polygonal regions in the shape of regular stars. Calculation of the Blaschke product dilatation allows a determination of the exact range of parameters that produce univalent mappings.
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