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.

Keywords

Delaunay triangulation, hyperbolic polyhedra, disk pattern

Mathematical Subject Classification 2000

Primary: 52C26

Secondary: 30F10

References

Forward citations

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

Volume 6, issue 1 (2002)

Gregory Leibon