On the Kobayashi and Carathéodory distance of bounded symmetric domains
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,\(\zeta\in D\).
hyperbolic Carathéodory-Kobayashi distance
scientific article; zbMATH DE number 4099669