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Holomorphic retracts of polyballs


Author: Tadeusz Kuczumow
Journal: Proc. Amer. Math. Soc. 98 (1986), 374-375
MSC: Primary 47H10; Secondary 32H15, 32H35
DOI: https://doi.org/10.1090/S0002-9939-1986-0854050-4
MathSciNet review: 854050
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Abstract: Let $ T$ be a holomorphic self-mapping in the Cartesian product $ {B^n}$ of $ n$ unit open balls in $ {{\mathbf{C}}^k}$. In this note we give a very short proof of the fact that if $ \operatorname{Fix} T = \{ y \in {B^n}:y = Ty\} $ is nonempty, then this set is a holomorphic retract of $ {B^n}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0854050-4
Keywords: Hyperbolic metric, nonexpansive mappings, holomorphic mappings, holomorphic retracts, fixed points
Article copyright: © Copyright 1986 American Mathematical Society

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