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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The extension of regular holomorphic maps


Author: H. L. Royden
Journal: Proc. Amer. Math. Soc. 43 (1974), 306-310
MSC: Primary 32D99; Secondary 32H15
DOI: https://doi.org/10.1090/S0002-9939-1974-0335851-X
MathSciNet review: 0335851
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Abstract: Let $ f$ be a holomorphic map of a $ k$-dimensional polydisk in $ {C^n}$ into an $ n$-dimensional complex manifold $ M$ which is regular at the origin. It is shown that $ f$ can be extended to a neighborhood in $ {C^n}$ of a slightly smaller polydisk so that the extension is also regular. If $ f$ is an embedding or immersion, then the extension may also be taken to be an embedding or immersion.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0335851-X
Keywords: Extension of holomorphic maps, holomorphic immersion, holomorphic embedding, equi-dimensional holomorphic maps
Article copyright: © Copyright 1974 American Mathematical Society