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On the Rigidity of Proper Holomorphic Self-Mappings of the Hua Domains

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Abstract

Hua domain, named after Chinese mathematician Loo-Keng Hua, is defined as a domain in \({\mathbb {C}}^n\) fibered over an irreducible bounded symmetric domain \(\Omega \subset {\mathbb {C}}^d\) with the fiber over \(z\in \Omega \) being a \((n-d)\)-dimensional generalized complex ellipsoid \(\Sigma (z)\). In 2015, Tu-Wang obtained the rigidity result that proper holomorphic mappings between two equidimensional Hua domains are biholomorphisms when the sets consisting of boundary points of Hua domains which are not strongly pseudoconvex have complex codimension at least 2. In this article, we find a counter-example to show that the rigidity result is not true for Hua domains without this condition and obtain the rigidity of proper holomorphic self-mappings of the Hua domains in this case.

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Acknowledgements

The author would like to thank Professor Zhenhan Tu for his helpful discussions, and thank the referees for useful comments. The author was supported by the National Natural Science Foundation of China (Nos. 11801187, 11871233 and 11871380).

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  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Lei Wang

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  1. Lei Wang
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Wang, L. On the Rigidity of Proper Holomorphic Self-Mappings of the Hua Domains. J Geom Anal 33, 235 (2023). https://doi.org/10.1007/s12220-023-01300-2

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