Extension property in the tridisc

Lukasz Kosinski; Wlodzimierz Zwonek

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arXiv · 1906.06607

Extension property in the tridisc

Lukasz Kosinski·Wlodzimierz Zwonek

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Abstract

Motivated by works on extension sets in standard domains we introduce a notion of the Carath\'eodory 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 which not only turns out to be Carath\'eodory 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 Carath\'eodory extremal problem is studied and new results on domains admitting (no) finite universal sets are given.

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Lukasz Kosinski, Wlodzimierz Zwonek. 2019-06-15. Extension property in the tridisc. https://arxiv.org/abs/1906.06607

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