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  • 1.
    Borell, Stefan
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    The Ball Embedding Property of the Open Unit Disc2011In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 130, no 10, p. 3573-3581Article in journal (Refereed)
    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.

  • 2.
    Borell, Stefan
    et al.
    University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.
    Kutzschebauch, Frank
    University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.
    Embeddings through Discrete Sets of Discs2008In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 46, no 2, p. 251-269Article in journal (Refereed)
    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.

  • 3.
    Borell, Stefan
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Kutzschebauch, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
    Non-equivalent embeddings into complex Euclidean spaces2006In: International Journal of Mathematics, ISSN 0129-167X, Vol. 17, no 9, p. 1033-1046Article in journal (Refereed)
    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.

  • 4. Borell, Stefan
    et al.
    Kutzschebauch, Frank
    Wold, Erlend Fornæss
    Proper Holomorphic Disks in the Complement of Varieties in C22008In: Mathematical Research Letters, ISSN 1073-2780, E-ISSN 1945-001X, Vol. 15, no 4, p. 821-826Article in journal (Refereed)
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