## Arkiv för Matematik

• Ark. Mat.
• Volume 54, Number 2 (2016), 299-319.

### The Hartogs extension theorem for holomorphic vector bundles and sprays

#### 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.

#### Note

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

#### Article information

Source
Ark. Mat., Volume 54, Number 2 (2016), 299-319.

Dates
Revised: 1 July 2015
First available in Project Euclid: 30 January 2017

https://projecteuclid.org/euclid.afm/1485802742

Digital Object Identifier
doi:10.1007/s11512-015-0226-y

Mathematical Reviews number (MathSciNet)
MR3546355

Zentralblatt MATH identifier
1364.32010

Rights

#### Citation

Andrist, Rafael B.; Shcherbina, Nikolay; Wold, Erlend F. The Hartogs extension theorem for holomorphic vector bundles and sprays. Ark. Mat. 54 (2016), no. 2, 299--319. doi:10.1007/s11512-015-0226-y. https://projecteuclid.org/euclid.afm/1485802742

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