Characterizing the Delaunay decompositions of compact hyperbolic surfaces

Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decomposition and angle assignment can be realized as the data of an actual Delaunay decomposition of a hyperbolic surface.