Geodesic
The Lowner-Kufarev representations for domains with analytic boundaries
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2.

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We consider the Lowner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Lowner-Kufarev chain consisting of univalent quadratic polynomials and compare the Lowner-Kufarev representations of bounded and arbitrary univalent functions.
Keywords: Lowner-Kufarev equation, analytic continuation, univalent polynomials, bounded univalent functions 
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Prokhorov, Dmitri. The Lowner-Kufarev representations for domains with analytic boundaries. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 65 (2011) no. 2. http://geodesic.mathdoc.fr/item/AUM_2011_65_2_a15/

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