# MathSciDoc: An Archive for Mathematician ∫

#### Algebraic GeometryFunctional 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.