The inner Carathéodory distance for the annulus. II (Q1310144)

Let \(A:=\{\lambda \in \mathbb{C}:1/R<| \lambda |<R\}\), \(c_ A:=\) the Carathéodory distance, \(c^ i_ A:=\) the inner Carathéodory distance on \(A\). We have proved [Math. Ann. 289 335-339 (1991; Zbl 0719.30036)], that \(c_ A (\lambda', \lambda'')=c^ i_ A (\lambda',\lambda'')\) iff \(\arg \lambda'=\arg \lambda''\). In the paper we continue studying the geometry of the space \((A,c^ i_ A)\), namely we present effective formulas for \(c^ i_ A\) and for geodesics with respect to \(c^ i_ A\).