Interpolation by holomorphic automorphisms and embeddings in Cn |
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Authors: | Franc Forstneric |
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Institution: | (1) Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | Let n > 1 and let
C
n
denote the complex n-dimensional Euclidean space. We prove several jet-interpolation results for nowhere degenerate entire
mappings F:C
n →C
n
and for holomorphic automorphisms of
C
n
on discrete subsets of
C
n.We also prove an interpolation theorem for proper holomorphic embeddings of Stein manifolds into
C
n.For each closed complex submanifold (or subvariety) M ⊂
C
n
of complex dimension m < n we construct a domain Ω ⊂C
n
containing M and a biholomorphic map F: Ω →
C
n
onto
C
n
with J F ≡ 1such that F(M) intersects the image of any nondegenerate entire map G:C
n−m →C
n
at infinitely many points. If m = n − 1, we construct F as above such that
C
n ∖F(M) is hyperbolic. In particular, for each m ≥ 1we construct proper holomorphic embeddings F:C
m →C
m−1
such that the complement
C
m+1 ∖F(C
m
)is hyperbolic. |
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Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 32H02 32H20 32M05 |
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