An embedding of C in C with hyperbolic complement
نویسندگان
چکیده
Let X be a closed, 1-dimensional, complex subvariety of C and let B be a closed ball in C −X. Then there exists a Fatou-Bieberbach domain Ω with X ⊆ Ω ⊆ C − B such that Ω − X is Kobayashi hyperbolic. In particular, there exists a biholomorphic map Φ : Ω → C such that C−Φ(X) is Kobayashi hyperbolic. As corollaries, there is an embedding of the plane in C whose complement is hyperbolic, and there is a nontrivial Fatou-Bieberbach domain containing any finite collection of complex lines.
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