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In mathematics, Grunsky's theorem, due to the German mathematician Helmut Grunsky, is a result in complex analysis concerning holomorphic univalent functions defined on the unit disk in the complex numbers. The theorem states that a univalent function defined on the unit disc, fixing the point 0, maps every disk |z| < r onto a starlike domain for r ≤ tanh π/4. The largest r for which this is true is called the radius of starlikeness of the function.

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  • Grunsky's theorem (en)
  • Grunskys sats (sv)
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  • In mathematics, Grunsky's theorem, due to the German mathematician Helmut Grunsky, is a result in complex analysis concerning holomorphic univalent functions defined on the unit disk in the complex numbers. The theorem states that a univalent function defined on the unit disc, fixing the point 0, maps every disk |z| < r onto a starlike domain for r ≤ tanh π/4. The largest r for which this is true is called the radius of starlikeness of the function. (en)
  • Inom matematiken är Grunskys sats, bevisad av den tyska matematikernn , ett resultat som säger att en analytisk funktion definierad på enhetsskivan som satisfierar f(0) = 0 som fixerar punkten 0 avbildar varje skiva |z| < r till ett stjärnformat område för r ≤ tanh π/4. Det största värdet på r för vilket detta gäller kallas 'radien av stjärnlikhet av funktionen. (sv)
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  • In mathematics, Grunsky's theorem, due to the German mathematician Helmut Grunsky, is a result in complex analysis concerning holomorphic univalent functions defined on the unit disk in the complex numbers. The theorem states that a univalent function defined on the unit disc, fixing the point 0, maps every disk |z| < r onto a starlike domain for r ≤ tanh π/4. The largest r for which this is true is called the radius of starlikeness of the function. (en)
  • Inom matematiken är Grunskys sats, bevisad av den tyska matematikernn , ett resultat som säger att en analytisk funktion definierad på enhetsskivan som satisfierar f(0) = 0 som fixerar punkten 0 avbildar varje skiva |z| < r till ett stjärnformat område för r ≤ tanh π/4. Det största värdet på r för vilket detta gäller kallas 'radien av stjärnlikhet av funktionen. (sv)
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