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<p>In this article, we study various properties of holomorphic retracts in Lempert domains. We associate the existence and the form of holomorphic retracts with the linear ones, provide non-trivial examples and discuss their properties in a quite general setting. Later we specialize to two Lempert domains which are the Lie ball of dimension three and its 2-proper holomorphic image, that is, the tetrablock and give a complete description of holomorphic retracts in these domains.</p>

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Holomorphic Retracts in the Lie Ball and the Tetrablock

  • 期刊论文

  • 发表日期：

    2025年3月6日

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  • Gargi Ghosh,
  • Włodzimierz Zwonek

摘要

In this article, we study various properties of holomorphic retracts in Lempert domains. We associate the existence and the form of holomorphic retracts with the linear ones, provide non-trivial examples and discuss their properties in a quite general setting. Later we specialize to two Lempert domains which are the Lie ball of dimension three and its 2-proper holomorphic image, that is, the tetrablock and give a complete description of holomorphic retracts in these domains.