Interpolation by holomorphic automorphisms and embeddings in Cn

Article

Abstract

Let n > 1 and letCndenote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire mappings F:CnCnand for holomorphic automorphisms ofCnon discrete subsets ofCn.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds intoCn.For each closed complex submanifold (or subvariety) M ⊂Cnof complex dimension m < n we construct a domain ΩCncontaining M and a biholomorphic map F: Ω →CnontoCnwith J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:Cn−mCnat infinitely many points. If m = n − 1, we construct F as above such thatCnF(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:CmCm−1such that the complementCm+1F(Cm)is hyperbolic.

Math Subject Classifications

32H02 32H20 32M05 

Key Words and Phrases

Holomorphic mapping automorphism interpolation embedding hyperbolic 

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Copyright information

© Mathematica Josephina, Inc. 1999

Authors and Affiliations

  1. 1.Institute of MathematicsPhysics and MechanicsLjubljanaSlovenia

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