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2 results

  • A Note about Analytic Solvability of Complex Planar Vector Fields with Degeneracies

  • Paulo L. Dattori da Silva
  • Journal:
    Canadian Mathematical Bulletin / Volume 54 / Issue 2 / 01 June 2011
    Published online by Cambridge University Press:
    20 November 2018, pp. 249-254
    Print publication:
    01 June 2011
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  • This paper deals with the analytic solvability of a special class of complex vector fields defined on the real plane, where they are tangent to a closed real curve, while off the real curve, they are elliptic.

  • Holomorphic diffeomorphisms of semisimple homogeneous spaces

  • Árpád Tóth, Dror Varolin
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 5 / September 2006
    Published online by Cambridge University Press:
    25 September 2006, pp. 1308-1326
    Print publication:
    September 2006
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  • We study the infinite-dimensional group of holomorphic diffeomorphisms of certain Stein homogeneous spaces. We show that holomorphic automorphisms can be approximated by generalized shears arising from unipotent subgroups. For the homogeneous spaces this implies the existence of Fatou–Bieberbach domains of the first and second kind, and the failure of the Abhyankar–Moh theorem for holomorphic embeddings.