Canadian Journal of Mathematics ( IF 0.7 ) Pub Date : 2020-02-24 , DOI: 10.4153/s0008414x20000139 Łukasz Kosiński , Włodzimierz Zwonek
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.
中文翻译:
扩展属性和通用集
受标准域中扩展集工作的启发,我们引入了 Carathéodory 集的概念,它似乎更适合用于扩展集表征结果证明中使用的方法。特别强调了三圆盘中的一类二维子流形,它不仅是 Carathéodory,而且还提供了著名的 Lempert 定理所适用的二维域的例子。此外,研究了最近引入的用于 Carathéodory 极值问题的通用集概念,并给出了关于允许(无)有限通用集的域的新结果。