Numerical methods of convex Lobachevsky geometry (Q2799760)

A natural extension of Euclidean convex geometry is convex geometry of Lobachevsky space \(H_{\kappa}\) of curvature \((-\kappa),\) with positive \(\kappa.\) To an arbitrary closed convex subset \(Q \subseteq H_{\kappa}\) can be assigned conformally-flat metrics of bounded curvature.NEWLINENEWLINEIn the paper, the following issues are studied:NEWLINENEWLINE{\parindent=7mm\begin{itemize}\item{}Mapping of conformally-flat metrics in the Lobachevsky space \(H_{\kappa}\).NEWLINENEWLINE\item{}Mapping of one-dimensional conformally-flat metrics in the Lobachevsky plane.NEWLINENEWLINE\item{}One-dimensional conformally-flat splines.NEWLINENEWLINE\end{itemize}} NEWLINENEWLINESeveral examples are given.NEWLINENEWLINEFor the entire collection see [Zbl 1298.53003].