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<p>Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations.</p><p>The paper reveals a deep connection between biunivalence and geometry of Teichmüller balls and provides some sufficient conditions for biunivalence of holomorphic functions on the disk. Among the consequences, one obtains new sharp distortion theorems for univalent functions with quasiconformal extension.</p>

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Teichmüller balls and biunivalent holomorphic functions

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Samuel L. Krushkal

摘要

Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations.

The paper reveals a deep connection between biunivalence and geometry of Teichmüller balls and provides some sufficient conditions for biunivalence of holomorphic functions on the disk. Among the consequences, one obtains new sharp distortion theorems for univalent functions with quasiconformal extension.