Rigidity of proper holomorphic self-mappings of the hexablock

2025/07/22 by Bi, Enchao, Shaaban, Zeinab, Su, Guicong
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.16176

Abstract

The hexablock \(ℍ\), introduced by Biswas-Pal-Tomar \citeHexablock, is a Hartogs domain in \(ℂ⁴\) fibered over the tetrablock \(𝔼\) in \(ℂ³\), 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 \citeHexablock.

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