Mathematische Zeitschrift

, Volume 277, Issue 1–2, pp 325–338 | Cite as

Oka properties of ball complements



Let \(n>1\) be an integer. We prove that holomorphic maps from Stein manifolds \(X\) of dimension \({<}n\) to the complement \(\mathbb {C}^n{\setminus } L\) of a compact convex set \(L\subset \mathbb {C}^n\) satisfy the basic Oka property with approximation and interpolation. If \(L\) is polynomially convex then the same holds when \(2\dim X \le n\). We also construct proper holomorphic maps, immersions and embeddings \(X\rightarrow \mathbb {C}^n\) with additional control of the range, thereby extending classical results of Remmert, Bishop and Narasimhan.


Oka principle Holomorphic flexibility Oka manifold Polynomial convexity 

Mathematics Subject Classification (2010)

Primary 32E10 32E20 32E30 32H02 Secondary 32Q99 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Institute of Mathematics, Physics, and MechanicsLjubljanaSlovenia
  3. 3.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia
  4. 4.Matematisk InstituttUniversitetet i OsloOsloNorway

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