Geodesic
Extension Property and Universal Sets
Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 717-736

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DOI

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.
DOI : 10.4153/S0008414X20000139
Mots-clés : extension set, Carathéodory set, Lempert theorem, universal set for the Carathéodory extremal problem 
Kosiński, Łukasz; Zwonek, Włodzimierz. Extension Property and Universal Sets. Canadian journal of mathematics, Tome 73 (2021) no. 3, pp. 717-736. doi: 10.4153/S0008414X20000139
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     year = {2021},
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