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Proper holomorphic embeddings into stein manifolds with the density property

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Abstract

We prove that a Stein manifold of dimension d admits a proper holomorphic embedding into any Stein manifold of dimension at least 2d + 1 satisfying the holomorphic density property. This generalizes classical theorems of Remmert, Bishop and Narasimhan, pertaining to embeddings into complex euclidean spaces, as well as several other recent results.

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Authors and Affiliations

  1. Bergische Universität Wuppertal, Fachbereich C - Mathematik und Naturwissenschaften, Gausstr. 20, D-42119, Wuppertal, Germany

    Rafael Andrist

  2. Faculty of Mathematics and Physics, and Institute of Mathematics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Franc Forstnerič

  3. School of Mathematical Sciences, University of Adelaide, Adelaide, SA, 5005, Australia

    Tyson Ritter

  4. Matematisk Institutt, Universitetet I Oslo, Postboks 1053 Blindern, 0316, Oslo, Norway

    Erlend Fornæss Wold

Authors
  1. Rafael Andrist
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  2. Franc Forstnerič
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  3. Tyson Ritter
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  4. Erlend Fornæss Wold
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Corresponding author

Correspondence to Rafael Andrist.

Additional information

F. Forstnerič is supported by research program P1-0291 and research grant J1-5432 from ARRS, Republic of Slovenia.

T. Ritter is supported by Australian Research Council grant DP120104110.

E. F. Wold is supported by grant NFR-209751/F20 from the Norwegian Research Council.

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Andrist, R., Forstnerič, F., Ritter, T. et al. Proper holomorphic embeddings into stein manifolds with the density property. JAMA 130, 135–150 (2016). https://doi.org/10.1007/s11854-016-0031-y

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  • DOI: https://doi.org/10.1007/s11854-016-0031-y

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