Characterizing the Delaunay decompositions of compact hyperbolic surfaces

Details Characterizing the Delaunay decompositions of compact hyperbolic surfaces Characterizing the Delaunay decompositions of compact hyperbolic surfaces

2001-03-26

arxiv.org/abs/math/0103174v2

Geom. Topol. 6(2002) 361-391

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper12.abs.html

Scientific paper

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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