Proper holomorphic mappings that must be rational
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- by Steven Bell PDF
- Trans. Amer. Math. Soc. 284 (1984), 425-429 Request permission
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
- Steven R. Bell, The Bergman kernel function and proper holomorphic mappings, Trans. Amer. Math. Soc. 270 (1982), no. 2, 685–691. MR 645338, DOI 10.1090/S0002-9947-1982-0645338-1
- Steven R. Bell, Proper holomorphic mappings between circular domains, Comment. Math. Helv. 57 (1982), no. 4, 532–538. MR 694605, DOI 10.1007/BF02565875
- Walter Rudin, Proper holomorphic maps and finite reflection groups, Indiana Univ. Math. J. 31 (1982), no. 5, 701–720. MR 667790, DOI 10.1512/iumj.1982.31.31050
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 284 (1984), 425-429
- MSC: Primary 32H35; Secondary 32H10
- DOI: https://doi.org/10.1090/S0002-9947-1984-0742433-5
- MathSciNet review: 742433