Extension property in the tridisc
Complex Variables
2020-02-19 v2
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.
Cite
@article{arxiv.1906.06607,
title = {Extension property in the tridisc},
author = {Lukasz Kosinski and Wlodzimierz Zwonek},
journal= {arXiv preprint arXiv:1906.06607},
year = {2020}
}
Comments
25 pages, the improved version with the new title, accepted for publication in the Canadian J. Math