Carathéodory balls and norm ball of the domains \(H_ n = \{ z\in\mathbb{C}^ n: | z_ 1| +\cdots +| z_ n| <1\}\)
type: Item
instance of: scholarly article
title: Carathéodory balls and norm ball of the domains \(H_ n = \{ z\in\mathbb{C}^ n: | z_ 1| +\cdots +| z_ n| <1\}\)
zbMATH Open document ID: 0824.32007
DOI: 10.1007/BF02808194
author: Włodzimierz Zwonek
published in: Israel Journal of Mathematics
publication date: 1995-05-15T00:00:00Z
review text: Let \(N_ n(z) = | z_ 1 | + \dots + | z_ n |\) and let \[ H_ n = \{z \in C^ n : \;N_ n(z) < 1\}. \] It is proved that the only Carathéodory balls in \(H_ n\), which are norm balls, are those centered at the origin. It is noted that the same result is proved in a paper by U. Srebro in the same volume.
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 755538
zbMATH Keywords: Carathéodory pseudodistance
zbMATH Keywords: \(c\)-geodesics
reviewed by: Alexander Russakovskij
MaRDI profile type: Publication
cites work: Invariant distances and metrics in complex analysis
cites work: Q4296232
cites work: La métrique de Kobayashi et la représentation des domaines sur la boule
cites work: Carathéodory balls and norm balls of the domain \(H=\{(z_ 1,z_ 2)\in \mathbb{C}^ 2:| z_ 1| +| z_ 2| < 1\}\)
full work available at URL: https://doi.org/10.1007/bf02808194
OpenAlex ID: W1986916758
description: scientific article; zbMATH DE number 755538