Geometry & Topology, Vol. 6 (2002) Paper no. 12, pages 361--391.

Characterizing the Delaunay decompositions of compact hyperbolic surfaces

Gregory Leibon

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

AMS subject classification. Primary: 52C26. Secondary: 30F10.

DOI: 10.2140/gt.2002.6.361

E-print: arXiv:math.GT/0103174

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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Gregory Leibon
Hinman Box 6188, Dartmouth College
Hanover NH 03755, USA
Email: leibon@dartmouth.edu

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