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
1993-01-01
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.File in questo prodotto:
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