Abstract
This paper is concerned with the rigidity of proper holomorphic self-mappings of some unbounded weakly pseudoconvex domain, called a generalized Fock–Bargmann–Hartogs domain, which is defined as a Hartogs domain fibered over with the fiber being a generalized complex ellipsoid. We develop a new technique to show that any proper holomorphic self-mapping of a generalized Fock–Bargmann–Hartogs domain must be an automorphism without the restriction of the dimension of each fiber. As a main contribution, we partly solve the rigidity problems for proper holomorphic self-mappings of generalized Fock–Bargmann–Hartogs domains.
Citation
Enchao Bi. Guicong Su. "RIGIDITY OF PROPER HOLOMORPHIC SELF-MAPPINGS OF SOME UNBOUNDED WEAKLY PSEUDOCONVEX HARTOGS DOMAIN." Rocky Mountain J. Math. 54 (1) 31 - 42, February 2024. https://doi.org/10.1216/rmj.2024.54.31
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