Interpolation by holomorphic automorphisms and embeddings in Cn
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Let n > 1 and letCndenote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire mappings F:Cn →Cnand 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 Ω ⊂Cncontaining M and a biholomorphic map F: Ω →CnontoCnwith J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:Cn−m →Cnat infinitely many points. If m = n − 1, we construct F as above such thatCn ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:Cm →Cm−1such that the complementCm+1 ∖F(Cm)is hyperbolic.
Math Subject Classifications32H02 32H20 32M05
Key Words and PhrasesHolomorphic mapping automorphism interpolation embedding hyperbolic
- Buzzard, G. and Forstneric, F. An interpolation theorem for holomorphic automorphisms ofC n. Preprint, 1996.Google Scholar
- Forstneric, F. Holomorphic automorphism groups ofC n: A survey.The Proceedings Complex Analysis and Geometry, Ancona, V., Ballico, E., and Silva, A., Eds., 173–200,Lecture Notes in Pure and Applied Mathematics,173, Marcel Dekker, New York, 1996.Google Scholar
- Forstneric, F., Globevnik, J., and Stensønes, B. Embedding holomorphic discs through discrete sets,Math. Ann.,304, 559–596, (1995).Google Scholar