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Transactions of the American Mathematical Society

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Proper holomorphic mappings that must be rational

Author: Steven Bell
Journal: Trans. Amer. Math. Soc. 284 (1984), 425-429
MSC: Primary 32H35; Secondary 32H10
MathSciNet review: 742433
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Abstract: Suppose $ f:{D_1} \to {D_2}$ is a proper holomorphic mapping between bounded domains in $ {{\mathbf{C}}^n}$. We shall prove that under certain circumstances $ f$ must be a rational mapping, i.e., that the $ n$ component functions $ {f_i}$ of $ f$ are rational functions.

References [Enhancements On Off] (What's this?)

  • [1] S. Bell, The Bergman kernel function and proper holomorphic mappings, Trans. Amer. Math. Soc. 270 (1982), 685-691. MR 645338 (83i:32033)
  • [2] -, Proper holomorphic mappings between circular domains, Comment. Math. Helv. 57 (1982), 532-538. MR 694605 (84m:32032)
  • [3] W. Rudin, Proper holomorphic maps and finite reflection groups, Indiana Math. J. 31 (1982), 701-720. MR 667790 (84d:32038)

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Article copyright: © Copyright 1984 American Mathematical Society

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