Extending holomorphic mappings from subvarieties in Stein manifolds

Details Extending holomorphic mappings from subvarieties in Stein manifolds Extending holomorphic mappings from subvarieties in Stein manifolds

2004-11-02

arxiv.org/abs/math/0411048v3

Ann. Inst. Fourier, Grenoble, 55, 3 (2005), 733-751

Mathematics

Complex Variables

Ann. Inst. Fourier, to appear

Scientific paper

Suppose that Y is a complex manifold with the property that any holomorphic map from a compact convex set in a complex Euclidean space C^n (for any n) to Y is a uniform limit of entire maps from C^n to Y. We prove that a holomorphic map from a closed complex subvariety X_0 in a Stein manifold X to the manifold Y extends to a holomorphic map of X to Y provided that it extends to a continuous map. We then establish the equivalence of four Oka-type properties of a complex manifold. We also generalize a theorem of Siu and Demailly on the existence of open Stein neighborhoods of Stein subvarieties in complex spaces.

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