Vol. 297, No. 2, 2018

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

Enchao Bi and Zhenhan Tu

Vol. 297 (2018), No. 2, 277–297
Abstract

A generalized Fock–Bargmann–Hartogs domain Dnm,p(μ) is defined as a domain fibered over n with the fiber over z n being a generalized complex ellipsoid Σz(m,p). In general, a generalized Fock–Bargmann–Hartogs domain is an unbounded nonhyperbolic domain 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.

Keywords
automorphism groups, Bergman kernels, generalized Fock–Bargmann–Hartogs domains, proper holomorphic mappings
Mathematical Subject Classification 2010
Primary: 32A07, 32A25, 32H35, 32M05
Milestones
Received: 23 October 2016
Revised: 24 July 2017
Accepted: 23 March 2018
Published: 20 December 2018
Authors
Enchao Bi
School of Mathematics and Statistics
Qingdao University
Qingdao
China
Zhenhan Tu
School of Mathematics and Statistics
Wuhan University
Wuhan
China