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

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.

References in corpus (1)

• Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains