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1 results

  • Extension Property and Universal Sets

  • Part of
  • Łukasz Kosiński, Włodzimierz Zwonek
  • Journal:
    Canadian Journal of Mathematics / Volume 73 / Issue 3 / June 2021
    Published online by Cambridge University Press:
    24 February 2020, pp. 717-736
    Print publication:
    June 2021
    • Article
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  • Motivated by works on extension sets in standard domains, we introduce a notion of the Carathéodory set that seems better suited for the methods used in proofs of results on characterization of extension sets. A special stress is put on a class of two-dimensional submanifolds in the tridisc that not only turns out to be Carathéodory but also provides examples of two-dimensional domains for which the celebrated Lempert Theorem holds. Additionally, a recently introduced notion of universal sets for the Carathéodory extremal problem is studied and new results on domains admitting (no) finite universal sets are given.