An embedding of the unit ball that does not embed into a Loewner chain

  • J. E. Fornæss
  • E. F. WoldEmail author


We construct a holomorphic embedding \(\phi :\mathbb B^3\rightarrow {\mathbb {C}}^3\) such that \(\phi ({\mathbb {B}}^3)\) is not Runge in any strictly larger domain. As a consequence, \(\mathcal S\ne {\mathcal {S}}^1\) for \(n=3\).

Mathematics Subject Classification

32E20 32E30 32H02 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsNTNUTrondheimNorway
  2. 2.Department of MathematicsUniversity of OsloOsloNorway

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