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arXiv · 1812.10600

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

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.

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Enchao Bi, Zhenhan Tu. 2018-12-27. Rigidity of proper holomorphic mappings between generalized Fock-Bargmann-Hartogs domains. https://arxiv.org/abs/1812.10600

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