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An interpolation theorem for proper holomorphic embeddings

Franc Forstneric·Bjorn Ivarsson·Frank Kutzschebauch·Jasna Prezelj
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Abstract

Given a Stein manifold X of dimension n>1, a discrete sequence a_j in X, and a discrete sequence b_j in C^m where m > [3n/2], there exists a proper holomorphic embedding of X into C^m which sends a_j to b_j for every j=1,2,.... This is the interpolation version of the embedding theorem due to Eliashberg, Gromov and Schurmann. The dimension m cannot be lowered in general due to an example of Forster.

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Franc Forstneric, Bjorn Ivarsson, Frank Kutzschebauch, Jasna Prezelj. 2007-08-16. An interpolation theorem for proper holomorphic embeddings. https://doi.org/10.1007/s00208-007-0087-1

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