# MathSciDoc: An Archive for Mathematician ∫

#### Functional AnalysisGeometric Analysis and Geometric Topologymathscidoc: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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