Characterizing the Delaunay decompositions of compact hyperbolic surfaces

By Gregory Leibon. 2001

94 citations recorded by the source corpus.

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 decompo- sition. 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.

Subfields: Computer Graphics and Computer-Aided Design, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/15bb170a2d34d0f1b306e91393ac7b51ecaa13ca

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In Computer Graphics and Computer-Aided Design

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Citations in the corpus

Variational principles for circle patterns and Koebe’s theorem (2002, background): “Similar results were obtained by Bowditch [Bow91], Garrett [Gar92], Rivin [Riv99], and Leibon [Lei01].”
Discrete conformal maps and ideal hyperbolic polyhedra (2010, unknown): “(5.9) This was shown by Leibon [18], who also showed that the volume function Vh is strictly concave on its domain of definition, (α1,α2,α3) ∈ R3 α1 > 0, α2 > 0, α3 > 0, α1+α2+α3 π .”
A discrete uniformization theorem for polyhedral surfaces II (2014, background): “On the other hand, Leibon showed in [15] that Dc(T ) is a cell.”
Rigidity of polyhedral surfaces, II (2006, background): “Results similar to Penner’s work have been established recently for hyperbolic cone metric by Leibon [8] and hyperbolic metric with geodesic boundary in [10].”
A variational principle for weighted Delaunay triangulations and hyperideal polyhedra (2006, methodology): “A variant of Rivin’s variational approach for Delaunay decompositions of hyperbolic surfaces was developed by Leibon [19].”