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arXiv · 2507.16176

Rigidity of proper holomorphic self-mappings of the hexablock

Enchao Bi·Zeinab Shaaban·Guicong Su
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Abstract

The hexablock \(\mathbb{H}\), introduced by Biswas-Pal-Tomar \cite{Hexablock}, is a Hartogs domain in \(\mathbb{C}^4\) fibered over the tetrablock \(\mathbb{E}\) in \(\mathbb{C}^3\), arising in the context of \(\mu\)-synthesis problems. In this paper, we prove that every proper holomorphic self-map of \(\mathbb{H}\) is necessarily an automorphism. Consequently, we resolve the conjecture \(G(\mathbb{H}) = \mathrm{Aut}(\mathbb{H})\) on the automorphism group structure, originally posed by Biswas-Pal-Tomar in \cite{Hexablock}.

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Enchao Bi, Zeinab Shaaban, Guicong Su. 2025-07-22. Rigidity of proper holomorphic self-mappings of the hexablock. https://arxiv.org/abs/2507.16176

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