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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The ball embedding property of the open unit disc


Author: Stefan Borell
Journal: Proc. Amer. Math. Soc. 139 (2011), 3573-3581
MSC (2010): Primary 32H02, 32Q40, 32Q45
Published electronically: February 14, 2011
MathSciNet review: 2813388
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Abstract: We prove that the open unit disc $ \triangle$ in  $ \mathbb{C}$ satisfies the ball embedding property in  $ \mathbb{C}^2$; i.e., given any discrete set of discs in  $ \mathbb{C}^2$ there exists a proper holomorphic embedding $ \triangle\hookrightarrow\mathbb{C}^2$ which passes arbitrarily close to the discs. It is already known that  $ \mathbb{C}$ does not satisfy the ball embedding property in  $ \mathbb{C}^2$ and that $ \triangle$ satisfies the ball embedding property in  $ \mathbb{C}^n$ for $ n>2$.


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Additional Information

Stefan Borell
Affiliation: Department of Mathematics, University of Berne, Sidlerstrasse 5, CH-3012 Berne, Switzerland
Address at time of publication: Department of Natural Sciences, Engineering and Mathematics, Mid Sweden University, SE-851 70 Sundsvall, Sweden
Email: stefan.borell@math.unibe.ch, stefan.borell@miun.se

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10798-6
PII: S 0002-9939(2011)10798-6
Received by editor(s): April 27, 2010
Received by editor(s) in revised form: August 26, 2010
Published electronically: February 14, 2011
Additional Notes: The author wishes to thank Frank Kutzschebauch and Erlend Fornæss Wold for fruitful discussions regarding this topic and the reviewer for helpful comments and remarks.
This work was supported by the Swiss National Science Foundation, grants 200020–124668/1 and PBBE2–121066.
Communicated by: Franc Forstneric
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.