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


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 \(n=3\).

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Correspondence to E. F. Wold.

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Fornæss, J.E., Wold, E.F. An embedding of the unit ball that does not embed into a Loewner chain. Math. Z. 296, 73–78 (2020).

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Mathematics Subject Classification

  • 32E20
  • 32E30
  • 32H02