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3 results

  • Uniformization and Steinness

  • Stefan Nemirovski, Rasul Gazimovich Shafikov
  • Journal:
    Canadian Mathematical Bulletin / Volume 61 / Issue 3 / 01 September 2018
    Published online by Cambridge University Press:
    20 November 2018, pp. 637-639
    Print publication:
    01 September 2018
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  • It is shown that the unit ball in ${{\mathbb{C}}^{n}}$ is the only complexmanifold that can universally cover both Stein and non-Stein strictly pseudoconvex domains.

  • Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

  • Part of
  • Fréderic Campana, Benoît Claudon, Philippe Eyssidieux
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 2 / February 2015
    Published online by Cambridge University Press:
    26 November 2014, pp. 351-376
    Print publication:
    February 2015
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  • We extend to compact Kähler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

  • Locally conformally Kähler metrics on Kato surfaces

  • Marco Brunella
  • Journal:
    Nagoya Mathematical Journal / Volume 202 / June 2011
    Published online by Cambridge University Press:
    11 January 2016, pp. 77-81
    Print publication:
    June 2011
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  • We show that every Kato surface admits a locally conformally Kähler metric.