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Borell, Stefan
Publications (4 of 4) Show all publications
Borell, S. (2011). The Ball Embedding Property of the Open Unit Disc. Proceedings of the American Mathematical Society, 130(10), 3573-3581
Open this publication in new window or tab >>The Ball Embedding Property of the Open Unit Disc
2011 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 130, no 10, p. 3573-3581Article in journal (Refereed) Published
Abstract [en]

We prove that the open unit disc Delta in C satisfies the ball embedding property in C(2); i.e., given any discrete set of discs in C(2) there exists a proper holomorphic embedding Delta hooked right arrow C(2) which passes arbitrarily close to the discs. It is already known that C does not satisfy the ball embedding property in C(2) and that Delta satisfies the ball embedding property in C(n) for n > 2.

National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-15028 (URN)10.1090/S0002-9939-2011-10798-6 (DOI)000295432600018 ()2-s2.0-79960748519 (Scopus ID)
Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2017-12-08Bibliographically approved
Borell, S. & Kutzschebauch, F. (2008). Embeddings through Discrete Sets of Discs. Arkiv för matematik, 46(2), 251-269
Open this publication in new window or tab >>Embeddings through Discrete Sets of Discs
2008 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 46, no 2, p. 251-269Article in journal (Refereed) Published
Abstract [en]

We investigate whether a Stein manifold M which allows proper holomorphic embedding into ℂ n can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of M is smaller than n/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.

National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-15026 (URN)10.1007/s11512-008-0079-8 (DOI)
Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2017-12-08Bibliographically approved
Borell, S., Kutzschebauch, F. & Wold, E. F. (2008). Proper Holomorphic Disks in the Complement of Varieties in C2. Mathematical Research Letters, 15(4), 821-826
Open this publication in new window or tab >>Proper Holomorphic Disks in the Complement of Varieties in C2
2008 (English)In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 4, p. 821-826Article in journal (Refereed) Published
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-15027 (URN)
Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2017-12-08Bibliographically approved
Borell, S. & Kutzschebauch, F. (2006). Non-equivalent embeddings into complex Euclidean spaces. International Journal of Mathematics, 17(9), 1033-1046
Open this publication in new window or tab >>Non-equivalent embeddings into complex Euclidean spaces
2006 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 17, no 9, p. 1033-1046Article in journal (Refereed) Published
Abstract [en]

We study the number of equivalence classes of proper holomorphic embeddings of a Stein space X into ℂn. In this paper we prove that if the automorphism group of X is a Lie group and there exists a proper holomorphic embedding of X into ℂn, 0 < dim X < n, then for any k ≥ 0 there exist uncountably many non-equivalent proper holomorphic embeddings Φ: X × ℂk ℂn × ℂk. For k = 0 all embeddings will be proved to satisfy the additional property of ℂn\Φ(X) being (n - dim X)-Eisenman hyperbolic. As a corollary we conclude that there are uncountably many non-equivalent proper holomorphic embeddings of ℂk into ℂn whenever 0 < k < n.

Keywords
proper holomorphic embeddings, hyperbolicity, Eisenman, complex analysis
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-3420 (URN)10.1142/S0129167X06003795 (DOI)000242603500002 ()2-s2.0-33750928991 (Scopus ID)3404 (Local ID)3404 (Archive number)3404 (OAI)
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2017-12-12Bibliographically approved
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