EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 75(89), pp. 9–24 (2004)

Previous Article

Next Article

Contents of this Issue

Other Issues


ELibM Journals

ELibM Home

EMIS Home


Pick a mirror

 

ON A PARAMETRIC METHOD FOR CONFORMAL MAPS WITH QUASICONFORMAL EXTENSIONS

Alexander Vasil'ev

Departamento de Matematica, Universidad Técnica Federico Santa Maria Casilla, 110-V, Valparaiso, Chile

Abstract: 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
© 2004–2005 ELibM for the EMIS Electronic Edition