The paper demonstrates that every holomorphic self-map of the hexablock is an automorphism, suggesting a specific group structure.
The hexablock \(H\), introduced by Biswas-Pal-Tomar {Hexablock}, is a Hartogs domain in \(C^4\) fibered over the tetrablock \(E\) in \(C^3\), arising in the context of \(μ\)-synthesis problems. In this paper, we prove that every proper holomorphic self-map of \(H\) is necessarily an automorphism. Consequently, we resolve the conjecture \(G(H) = Aut(H)\) on the automorphism group structure, originally posed by Biswas-Pal-Tomar in {Hexablock}.
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Bi et al. (2025) studied this question.
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