February 2024 RIGIDITY OF PROPER HOLOMORPHIC SELF-MAPPINGS OF SOME UNBOUNDED WEAKLY PSEUDOCONVEX HARTOGS DOMAIN
Enchao Bi, Guicong Su
Rocky Mountain J. Math. 54(1): 31-42 (February 2024). DOI: 10.1216/rmj.2024.54.31

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 n 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

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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

Information

Received: 7 August 2022; Accepted: 6 December 2022; Published: February 2024
First available in Project Euclid: 28 February 2024

MathSciNet: MR4718503
Digital Object Identifier: 10.1216/rmj.2024.54.31

Subjects:
Primary: 32A10‎ , 32H35

Keywords: generalized Fock–Bargmann–Hartogs domain , proper holomorphic self-mappings , unbounded weakly pseudoconvex domain

Rights: Copyright © 2024 Rocky Mountain Mathematics Consortium

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Vol.54 • No. 1 • February 2024
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