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Characterizing the Delaunay decompositions of compact
hyperbolic surfaces
Gregory Leibon
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Geometry & Topology 6 (2002)
361–391
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Abstract
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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.
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Keywords
Delaunay triangulation, hyperbolic
polyhedra, disk pattern
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Mathematical Subject Classification
Primary: 52C26
Secondary: 30F10
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Publication
Received: 28 March 2001
Revised: 8 July 2002
Accepted: 9 July 2002
Published: 13 July 2002
Proposed: Jean-Pierre Otal
Seconded: Benson Farb, Walter Neumann
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