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arXiv · 1801.07645

Runge tubes in Stein manifolds with the density property

Franc Forstneric·Erlend F. Wold
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Abstract

In this paper we give a very 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 $A$ of codimension at least two in a complex Euclidean space $\mathbb C^n$, the normal bundle of $A$ in $\mathbb C^n$ admits a holomorphic embedding onto a Runge domain in $\mathbb C^n$ which agrees with the inclusion map $A\hookrightarrow \mathbb C^n$ on the zero section.

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Franc Forstneric, Erlend F. Wold. 2018-01-23. Runge tubes in Stein manifolds with the density property. https://doi.org/10.1090/proc/14309

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