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Complex Analysis and Operator Theory

, Volume 11, Issue 7, pp 1491–1501 | Cite as

General Distortion Theorem for Univalent Functions with Quasiconformal Extension

  • Samuel L. KrushkalEmail author
Article

Abstract

One of the long-standing problems in the quasiconformal theory is finding sharp distortion bounds for k-quasiconformal maps for arbitrary \(k <1\). We provide a general distortion theorem for univalent functions in arbitrary quasiconformal disks with k-quasiconformal extensions to \(\mathbb {C}\) giving a universal power bound. Generically, this power cannot be strengthened.

Keywords

Univalent Quasiconformal Teichmüller space Infinite dimensional holomorphy Invariant metrics Complex geodesic Grunsky inequalities Variational problem Functional 

Mathematics Subject Classification

Primary: 30C55 30C62 30C75 30F60 32F45 Secondary: 30F45 46G20 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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