Geometry & Topology, Vol. 6 (2002)
Paper no. 12, pages 361--391.
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.
Delaunay triangulation, hyperbolic polyhedra, disk pattern
AMS subject classification.
Submitted to GT on 28 March 2001.
(Revised 8 July 2002.)
Paper accepted 9 July 2002.
Paper published 13 July 2002.
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