Abstract
The Fock–Bargmann–Hartogs domain Dn,m(μ) (μ>0) in Cn+m is defined by the inequality ‖w‖2<e−μ‖z‖2, where (z,w)∈Cn×Cm, which is an unbounded non-hyperbolic domain in Cn+m. Recently, Yamamori gave an explicit formula for the Bergman kernel of the Fock–Bargmann–Hartogs domains in terms of the polylogarithm functions and Kim–Ninh–Yamamori determined the automorphism group of the domain Dn,m(μ). In this article, we obtain rigidity results on proper holomorphic mappings between two equidimensional Fock–Bargmann–Hartogs domains. Our rigidity result implies that any proper holomorphic self-mapping on the Fock–Bargmann–Hartogs domain Dn,m(μ) with m≥2 must be an automorphism.
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