On the Kobayashi and Carathéodory distance of bounded symmetric domains
type: Item
instance of: scholarly article
title: On the Kobayashi and Carathéodory distance of bounded symmetric domains
zbMATH Open document ID: 0672.32010
author: Yoshihisa Kubota
published in: Kodai Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let D be a bounded symmetric domain, given in a canonical realization, in \({\mathbb{C}}^ n\), let \(k_ D\) be its hyperbolic Carathéodory-Kobayashi distance, and let Aut(D) denote the group of holomorphic automorphisms of D. We set \(rD=\{rz:\) \(z\in D\}\) for \(0<r<1\). The author shows that \[ rD=\{z\in D:\quad k_ D(z,0)<\tanh^{-1}r\},\quad 0<r<1, \] and \[ k_ D(z,\zeta)=\inf \{\tanh^{-1}r:\quad 0<r<1\quad and\quad \phi (z)\in rD\quad for\quad some\quad \phi \in Aut(D)\quad with\quad \phi (\zeta)=0\}, \] for every z,\(\zeta\in D\).
Mathematics Subject Classification ID: 32F45
Mathematics Subject Classification ID: 32Q45
Mathematics Subject Classification ID: 32M15
zbMATH DE Number: 4099669
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: hyperbolic Carathéodory-Kobayashi distance
reviewed by: Jacob Burbea
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038988
OpenAlex ID: W2059640728
cites work: Q3846750
cites work: Invariant distances on complex manifolds and holomorphic mappings
cites work: Q5608188
cites work: Realization of Hermitian symmetric spaces as generalized half-planes
cites work: Q5628476
cites work: Q3958740
DOI: 10.2996/KMJ/1138038988
description: scientific article; zbMATH DE number 4099669