Open Access
October 2016 The Hartogs extension theorem for holomorphic vector bundles and sprays
Rafael B. Andrist, Nikolay Shcherbina, Erlend F. Wold
Author Affiliations +
Ark. Mat. 54(2): 299-319 (October 2016). DOI: 10.1007/s11512-015-0226-y


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 Cn,n3, is not subelliptic.

Funding Statement

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


Download Citation

Rafael B. Andrist. Nikolay Shcherbina. Erlend F. Wold. "The Hartogs extension theorem for holomorphic vector bundles and sprays." Ark. Mat. 54 (2) 299 - 319, October 2016.


Received: 4 December 2014; Revised: 1 July 2015; Published: October 2016
First available in Project Euclid: 30 January 2017

zbMATH: 1364.32010
MathSciNet: MR3546355
Digital Object Identifier: 10.1007/s11512-015-0226-y

Rights: 2015 © Institut Mittag-Leffler

Vol.54 • No. 2 • October 2016
Back to Top