On the Teichmüller-Kühnau Extension of Univalent Functions

On the Teichmüller-Kühnau Extension of Univalent Functions

We give a complete description of the class of univalent holomorphic functions with regular quasiconformal extensions for which the Grunsky inequalities are both necessary and sufficient. This concerns the question posed by several authors.

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Veröffentlicht in:Georgian mathematical journal 2000-12, Vol.7 (4), p.723-729
1. Verfasser: Krushkal, S. L.
Format: Artikel
Sprache:eng
Schlagworte:
Carathéodory metric
extremal Teichmüller map
Fredholm eigenvalues
quasiconformal map
Univalent function
universal Teichmüller space
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Beschreibung
Zusammenfassung:We give a complete description of the class of univalent holomorphic functions with regular quasiconformal extensions for which the Grunsky inequalities are both necessary and sufficient. This concerns the question posed by several authors.
ISSN:1072-947X
1072-9176
1572-9176
DOI:10.1515/GMJ.2000.723