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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0742433-5
PII: S 0002-9947(1984)0742433-5
Article copyright: © Copyright 1984 American Mathematical Society