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Runge tubes in Stein manifolds with the density property


Authors: Franc Forstnerič and Erlend Fornæss Wold
Journal: Proc. Amer. Math. Soc. 148 (2020), 569-575
MSC (2010): Primary 32E30, 32H02; Secondary 32E10, 32M17, 14R10
DOI: https://doi.org/10.1090/proc/14309
Published electronically: November 6, 2019
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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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Additional Information

Franc Forstnerič
Affiliation: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI–1000 Ljubljana, Slovenia—and—Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI–1000 Ljubljana, Slovenia
Email: franc.forstneric@fmf.uni-lj.si

Erlend Fornæss Wold
Affiliation: Department of Mathematics, University of Oslo, Postboks 1053 Blindern, NO-0316 Oslo, Norway
Email: erlendfw@math.uio.no

DOI: https://doi.org/10.1090/proc/14309
Received by editor(s): January 23, 2018
Received by editor(s) in revised form: January 30, 2018, June 7, 2018, and June 29, 2018
Published electronically: November 6, 2019
Additional Notes: The first author was partially supported by the research grants P1-0291 and J1-7256 from ARRS, Republic of Slovenia.
The second author was supported by the RCN grant 240569, Norway.
Communicated by: Filippo Bracci
Article copyright: © Copyright 2019 American Mathematical Society