Proper holomorphic maps of bounded two-dimensional Reinhardt domains. I
- Authors: Kruzhilin N.G.1
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 85, No 3 (2021)
- Pages: 52-72
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133846
- DOI: https://doi.org/10.4213/im9066
- ID: 133846
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Abstract
The structure of proper holomorphic maps with multiplicity higher than one from bounded Reinhardt domains in $\mathbb C^2$ onto two-dimensional complex manifolds is described.
About the authors
Nikolai Georgievich Kruzhilin
Steklov Mathematical Institute of Russian Academy of Sciences
Email: kruzhil@mi-ras.ru
Doctor of physico-mathematical sciences
References
- K. Reinhardt, “Über Abbildungen durch analytische Funktionen zweier Veranderlichen”, Math. Ann., 83:3-4 (1921), 211–255
- Н. Г. Кружилин, “Голоморфные автоморфизмы гиперболических областей Рейнхарта”, Изв. АН СССР. Сер. матем., 52:1 (1988), 16–40
- S. Shimizu, “Automorphisms of bounded Reinhardt domains”, Japan J. Math. (N.S.), 15:2 (1989), 385–414
- P. Thullen, “Zu den Abbildungen durch analytische Funktionen mehrerer komplexer Veränderlichen Die Invarianz des Mittelpunktes von Kreiskörpern”, Math. Ann., 104:1 (1931), 244–259
- П. А. Солдаткин, “Голоморфная эквивалентность областей Рейнхарта в $mathbb C^2$”, Изв. РАН. Сер. матем., 66:6 (2002), 187–222
- D. E. Barrett, “Holomorphic equivalence and proper mapping of bounded Reinhardt domains not containing the origin”, Comment. Math. Helv., 59:4 (1984), 550–564
- E. Bedford, J. Dadok, “Proper holomorphic mappings and real reflection groups”, J. Reine Angew. Math., 1985:361 (1985), 1–82
- F. Berteloot, S. Pinchuk, “Proper holomorphic mappings between bounded complete Reinhardt domains in $mathbf C^2$”, Math. Z., 219:3 (1995), 343–356
- G. Dini, A. Selvaggi Primicerio, “Proper holomorphic mappings between generalized pseudoellipsoids”, Ann. Mat. Pura Appl. (4), 158 (1991), 219–229
- Kang-Tae Kim, M. Landucci, A. F. Spiro, “Factorization of proper holomorphic mappings through Thullen domains”, Pacific J. Math., 189:2 (1999), 293–310
- M. Landicci, A. Spiro, “Proper holomorphic maps between complete Reinhardt domains in $mathbb C^2$”, Complex Variables Theory Appl., 29:1 (1996), 9–28
- A. Isaev, N. G. Kruzhilin, “Proper holomorphic maps between Reinhardt domains in $mathbb C^2$”, Michigan Math. J., 54:1 (2006), 33–64
- A. Spiro, “Classification of proper holomorphic maps between Reinhardt domains in $mathbb C^2$”, Math. Z., 227:1 (1998), 27–44
- Н. Г. Кружилин, “Обобщение теоремы Кернера о собственных отображениях”, УМН, 65:6(396) (2010), 187–188
- S. R. Bell, “The Bergman kernel function and proper holomorphic mappings”, Trans. Amer. Math. Soc., 270:2 (1982), 685–691
- M. Landucci, “Proper holomorphic mappings between some nonsmooth domains”, Ann. Mat. Pura Appl. (4), 155 (1989), 193–203
- E. Bedford, S. Bell, “Extension of proper holomorphic mappings past the boundary”, Manuscripta Math., 50 (1985), 1–10
- E. Bedford, S. Bell, “Boundary behavior of proper holomorphic correspondences”, Math. Ann., 272:4 (1985), 505–518
- А. В. Лобода, “Всякая голоморфно-однородная трубка в $C^2$ имеет аффинно-однородное основание”, Сиб. матем. журн., 42:6 (2001), 1335–1339
- J. Dadok, P. Yang, “Automorphisms of tube domains and spherical tube hypersurfaces”, Amer. J. Math., 107:4 (1985), 999–1013
- M. Newman, Integral matrices, Pure Appl. Math., 45, Academic Press, New York–London, 1972, xvii+224 pp.
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