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Extremal partitions and distortion under the Montel bounded univalent maps

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

Alexander Vasil'ev
Alexander Vasil'ev
Affiliation:
Departmento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile e-mail: avassili@mat.utfsm.cl
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Abstract

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Extremal partitions of domains into configurations of certain to pological form are studied. The extremal value of the weighted sum of reduced moduli of circular domains and digons is obtained. These results are applied to some problems about distortion under bounded conformal maps of the unit disk with two preassigned values.

Keywords

moduli methodextremal problemunivalent functionMontel functiondistortion

MSC classification

Secondary: 30C75: Extremal problems for conformal and quasiconformal mappings, other methods 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 3 , December 2002 , pp. 419 - 432
Copyright
Copyright © Australian Mathematical Society 2002

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