Abstract
We characterize the existence of proper holomorphic mappings in the special class of bounded (1, 2, . . . , n)-balanced domains in \({\mathbb C^n,}\) called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groups of these domains.
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Acknowledgements
The author is greatly indebted to Ł. Kosiński for many stimulating conversations.
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The research was partially supported by the Research Grant No. N N201 361436 of the Polish Ministry of Science and Higher Education.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Zapałowski, P. Proper holomorphic mappings between symmetrized ellipsoids. Arch. Math. 97, 373–384 (2011). https://doi.org/10.1007/s00013-011-0311-9
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DOI: https://doi.org/10.1007/s00013-011-0311-9