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  • 1.
    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.

  • 2.
    Lind, Andreas
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.
    Porten, Egmont
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics. Uniwersytet Jana Kochanowskiego Kielcach, Inst Matemat, Kielce, Poland.
    On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces2016In: International Journal of Mathematics, ISSN 0129-167X, Vol. 27, no 6, article id 1650051Article in journal (Refereed)
    Abstract [en]

    On a normal Stein variety X, we study the thickening problem, i.e. the problem whether the assumption that a compact set K is contained in the interior of another compact set, L implies that the same inclusion holds for their holomorphic hulls. An affirmative answer is given for X with isolated quotient singularities. On any Stein space X with isolated singularities, we prove thickening for those hulls which have analytic structure at the singular points, obtaining a limitation for possible counter-examples. In dimension 2, we finally relate the holomorphic hulls to analytic extension from parts of strictly pseudoconvex boundaries.

  • 3.
    Merker, Joël
    et al.
    Ecole Normale Superiore Paris.
    Porten, Egmont
    Metrically Thin Singularities of Integrable CR Functions2000In: International Journal of Mathematics, ISSN 0129-167X, Vol. 11, no 7, p. 857-872Article in journal (Refereed)
    Abstract [en]

    In this article, we consider metrically thin singularities E of the solutions of the tangential Cauchy-Riemann operators on a smoothly embedded Cauchy-Riemann manifold M (CR functions on M \ E). Our main result establishes the removability of E within the space of locally integrable functions on M, which are CR on M\E, under the hypothesis that the (dim M - 2)-dimensional Hausdorff volume of E is zero and that the CR-orbits of M and of M \ E are comparable. [ABSTRACT FROM AUTHOR

  • 4.
    Wikström, Frank
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    The Dirichlet problem for maximal plurisubharmonic functions on analytic varieties in C-n2009In: International Journal of Mathematics, ISSN 0129-167X, Vol. 20, no 4, p. 521-528Article in journal (Refereed)
    Abstract [en]

    Let Omega be a B-regular domain in C-n and let V be a locally irreducible analytic variety in Omega. Given a continuous function phi is an element of C((V) over bar boolean AND partial derivative Omega), we prove that there is a unique maximal plurisubharmonic function u on V with boundary values given by f and furthermore that u is continuous on (V) over bar.

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