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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Characterizing the Delaunay decompositions of compact hyperbolic surfaces

Gregory Leibon

Geometry & Topology 6 (2002) 361–391

arXiv: math.GT/0103174

Abstract

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.

Keywords
Delaunay triangulation, hyperbolic polyhedra, disk pattern
Mathematical Subject Classification 2000
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
Authors
Gregory Leibon
Hinman Box 6188
Dartmouth College
Hanover
New Hampshire 03755
USA