Arkiv för Matematik

, Volume 53, Issue 2, pp 259–270 | Cite as

Fatou–Bieberbach domains in \(\mathbb{C}^{n}\setminus\mathbb{R}^{k}\)



We construct Fatou–Bieberbach domains in \(\mathbb{C}^{n}\) for n>1 which contain a given compact set K and at the same time avoid a totally real affine subspace L of dimension <n, provided that KL is polynomially convex. By using this result, we show that the domain \(\mathbb{C}^{n}\setminus\mathbb{R}^{k}\) for 1≤k<n enjoys the basic Oka property with approximation for maps from any Stein manifold of dimension <n.


Pseudoconvex Domain Stein Manifold Carleman Approximation Holomorphic Automorphism Exhaustion Function 
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© Institut Mittag-Leffler 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Institute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  3. 3.Department of MathematicsUniversity of OsloOsloNorway

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