PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)Vol. 75(89), pp. 9–24 (2004)
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PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.) Vol. 75(89), pp. 9–24 (2004) |
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ON A PARAMETRIC METHOD FOR CONFORMAL MAPS WITH QUASICONFORMAL EXTENSIONSAlexander Vasil'evDepartamento de Matematica, Universidad Técnica Federico Santa Maria Casilla, 110-V, Valparaiso, ChileAbstract: 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. Keywords: univalent function, quasiconformal map, Löwner-Kufarev equation, universal Teichmüller space Classification (MSC2000): 30C35, 30C62; 30F60 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 27 Oct 2004. This page was last modified: 22 Feb 2005.
© 2004 Mathematical Institute of the Serbian Academy of Science and Arts
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