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<p>The Grunsky operator arises from univalence and plays a crucial role in geometric function theory. This operator also implies quasiconformal extendibility and has an intrinsic connection with Teichmüller space theory and its interactions with complex analysis and pluripotential theory.</p><p>This paper surveys the recent results in this field and simultaneously provides the solutions of two old problems.</p>

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The Grunsky operator and quasiconformality: old and new

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Samuel L. Krushkal

摘要

The Grunsky operator arises from univalence and plays a crucial role in geometric function theory. This operator also implies quasiconformal extendibility and has an intrinsic connection with Teichmüller space theory and its interactions with complex analysis and pluripotential theory.

This paper surveys the recent results in this field and simultaneously provides the solutions of two old problems.