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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of hyperbolic manifolds


Author: Marco Abate
Journal: Proc. Amer. Math. Soc. 117 (1993), 789-793
MSC: Primary 32H20
MathSciNet review: 1128723
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Abstract: In this note we prove that a complex manifold $ X$ is Kobayashi hyperbolic if and only if the space $ \operatorname{Hol} (\Delta ,X)$ of holomorphic maps of the unit disk $ \Delta $ into $ X$ is relatively compact (with respect to the compact-open topology) in the space $ C(\Delta ,{X^{\ast}})$ of continuous maps from $ \Delta $ into the one-point compactification $ {X^{\ast}}$ of $ X$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1128723-6
PII: S 0002-9939(1993)1128723-6
Keywords: Hyperbolic manifolds, taut manifolds, Kobayashi distance
Article copyright: © Copyright 1993 American Mathematical Society