Article contents
Extension Property and Universal Sets
Published online by Cambridge University Press: 24 February 2020
Abstract
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.
Keywords
MSC classification
- Type
- Article
- Information
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Copyright
- © Canadian Mathematical Society 2020
Footnotes
The first author is partially supported by NCN grant SONATA BIS no. 2017/26/E/ST1/00723. The second author is partially supported by the OPUS grant no. 2015/17/B/ST1/00996 of the National Science Centre, Poland.
References
- 3
- Cited by