Rigidity of proper holomorphic mappings between generalized Fock–Bargmann–Hartogs domains
Rigidity of proper holomorphic mappings between generalized Fock–Bargmann–Hartogs domains
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DOI：
10.2140/pjm.2018.297.277
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发表时间：
2018-12
影响因子：
0.6
通讯作者：
Enchao Bi;Zhenhan Tu
中科院分区：
文献类型：
--
作者：
Enchao Bi;Zhenhan Tu
广义Fock-Bargmann-Hartogs域$D_n^{\mathbf{m}，\mathbf{p}}$被定义为在$\mathbb {C}^{n}$上纤维化的域，其中在$z\in \mathbb{C}^{n}$上的纤维是广义复椭球$\Sigma_z（{\mathbf{m}，\mathbf{p}}）$。广义Fock-Bargmann-Hartogs域一般是无界的非双曲域，没有光滑边界。本文的主要贡献如下。利用广义Fock-Bargmann-Hartogs域的Bergman核的显式公式，得到了两个等维广义Fock-Bargmann-Hartogs域之间的真全纯映射的刚性结果.因此，我们展示了一个例子，无界弱伪凸域上的正常全纯映射的刚性结果可以建立。
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.