Coresets for Continuous $k$-Center in Hyperbolic Space

We study the continuous $k$-center problem in fixed-dimensional hyperbolic space. The input is a finite point set $P \subset \mathbb H^D$, while the centers may be placed anywhere in the ambient space. A nonempty subset $P_\varepsilon\subseteq P$ is an $\varepsilon$-coreset if every exact optimal co