The Hartogs extension theorem for holomorphic vector bundles and sprays

Rafael B. Andrist Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Nikolay Shcherbina Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal Erlend F. Wold Matematisk Institutt, Universitet i Oslo

Algebraic Geometry Functional Analysis Geometric Analysis and Geometric Topology mathscidoc:1701.01010

Arkiv for Matematik, 1-21, 2014.12
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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@inproceedings{rafael2014the,
  title={The Hartogs extension theorem for holomorphic vector bundles and sprays},
  author={Rafael B. Andrist, Nikolay Shcherbina, and Erlend F. Wold},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406573966815},
  booktitle={Arkiv for Matematik},
  pages={1-21},
  year={2014},
}
Rafael B. Andrist, Nikolay Shcherbina, and Erlend F. Wold. The Hartogs extension theorem for holomorphic vector bundles and sprays. 2014. In Arkiv for Matematik. pp.1-21. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406573966815.
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