Runge tubes in Stein manifolds with the density property

Forstnerič, Franc; Wold, Erlend

doi:10.1090/proc/14309

Runge tubes in Stein manifolds with the density property
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by Franc Forstnerič and Erlend Fornæss Wold PDF

Proc. Amer. Math. Soc. 148 (2020), 569-575 Request permission

Abstract:

In this paper we give a simple proof of the existence and plenitude of Runge tubes in $\mathbb {C}^n$ $(n>1)$ and, more generally, in Stein manifolds with the density property. We show in particular that for any algebraic submanifold $X$ of codimension at least two in a complex Euclidean space $\mathbb {C}^n$, the normal bundle of $X$ admits a holomorphic embedding onto a Runge domain in $\mathbb {C}^n$ which agrees with the inclusion map $X\hookrightarrow \mathbb {C}^n$ on the zero section.

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