In this note we prove that a complex manifold X is Kobayashi hyperbolic if and only if the space 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*) of continuous maps from DELTA into the one-point compactification X* of X.

A CHARACTERIZATION OF HYPERBOLIC MANIFOLDS

ABATE, MARCO
1993

Abstract

In this note we prove that a complex manifold X is Kobayashi hyperbolic if and only if the space 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*) of continuous maps from DELTA into the one-point compactification X* of X.
Abate, Marco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/25859
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