Geodesic
On a Parametric Method for Conformal Maps with Quasiconformal Extensions
Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 9 .

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The Löwner-Kufarev equation gives a complete description of the class $S$ of all univalent holomorphic functions $f$ in the unit disk normalized by $f(0)+1=f'(0)=1$. We consider the class $S^{qc}$ of all functions from $S$ that admit quasiconformal extension to the whole Riemann sphere fixing $\infty$. There is a well known Becker's sufficient condition for the Löwner-Kufarev equation that guarantees a function from $S$ to be from $S^{qc}$. We study subordination chains of quasidisks bounded by analytic curves and corresponding motions on the modelling universal Teichmüller space. This leads to a specific form of the Löwner-Kufarev equation.
DOI : 10.2298/PIM0475009V
Classification : 30C35 30C62 30F60
Keywords: univalent function, quasiconformal map, Löwner-Kufarev equation, universal Teichmüller space 
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     author = {Alexander Vasilev},
     title = {On a {Parametric} {Method} for {Conformal} {Maps} with {Quasiconformal} {Extensions}},
     journal = {Publications de l'Institut Math\'ematique},
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Alexander Vasilev. On a Parametric Method for Conformal Maps with Quasiconformal Extensions. Publications de l'Institut Mathématique, _N_S_75 (2004) no. 89, p. 9 . doi : 10.2298/PIM0475009V. http://geodesic.mathdoc.fr/articles/10.2298/PIM0475009V/

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