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The Hartogs extension theorem for holomorphic vector bundles and sprays

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Arkiv för Matematik

Abstract

We give a detailed proof of Siu’s theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this result to study ellipticity properties of complements of compact subsets in Stein manifolds. In particular we show that the complement of a closed ball in \(\mathbb{C}^{n}, n \geq3\), is not subelliptic.

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Authors and Affiliations

  1. Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstraße 20, 42119, Wuppertal, Germany

    Rafael B. Andrist & Nikolay Shcherbina

  2. Matematisk Institutt, Universitet i Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    Erlend F. Wold

Authors
  1. Rafael B. Andrist
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  2. Nikolay Shcherbina
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  3. Erlend F. Wold
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Corresponding author

Correspondence to Rafael B. Andrist.

Additional information

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

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Andrist, R.B., Shcherbina, N. & Wold, E.F. The Hartogs extension theorem for holomorphic vector bundles and sprays. Ark Mat 54, 299–319 (2016). https://doi.org/10.1007/s11512-015-0226-y

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  • DOI: https://doi.org/10.1007/s11512-015-0226-y

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