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Mathematics > Complex Variables

arXiv:1812.10600 (math)
[Submitted on 27 Dec 2018]

Title:Rigidity of proper holomorphic mappings between generalized Fock-Bargmann-Hartogs domains

Authors:Enchao Bi, Zhenhan Tu
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Abstract:A generalized Fock-Bargmann-Hartogs domain $D_n^{\mathbf{m},\mathbf{p}}$ is defined as a domain fibered over $\mathbb{C}^{n}$ with the fiber over $z\in \mathbb{C}^{n}$ being a generalized complex ellipsoid $\Sigma_z({\mathbf{m},\mathbf{p}})$. In general, a generalized Fock-Bargmann-Hartogs domain is an unbounded non-hyperbolic domains without smooth boundary. The main contribution of this paper is as follows. By using the explicit formula of Bergman kernels of the generalized Fock-Bargmann-Hartogs domains, we obtain the rigidity results of proper holomorphic mappings between two equidimensional generalized Fock-Bargmann-Hartogs domains. We therefore exhibit an example of unbounded weakly pseudoconvex domains on which the rigidity results of proper holomorphic mappings can be built.
Subjects: Complex Variables (math.CV)
Cite as: arXiv:1812.10600 [math.CV]
  (or arXiv:1812.10600v1 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1812.10600
Journal reference: Pacific J. Math. 297(2018), 277-297

Submission history

From: Zhenhan Tu [view email]
[v1] Thu, 27 Dec 2018 02:41:35 UTC (16 KB)
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