Characterizing the Delaunay decompositions of compact hyperbolic surfaces

@article{Leibon2002CharacterizingTD,
  title={Characterizing the Delaunay decompositions of compact hyperbolic surfaces},
  author={Gregory Leibon},
  journal={Geometry \& Topology},
  year={2002},
  volume={6},
  pages={361-391}
}
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. 
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References

SHOWING 1-10 OF 28 REFERENCES
Random Delaunay triangulations, the Thurston-Andreev theorem, and metric uniformization
In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures howExpand
Random Delaunay triangulations and metric uniformization
In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In aExpand
The decorated Teichmüller space of punctured surfaces
A principal ℝ+5-bundle over the usual Teichmüller space of ans times punctured surface is introduced. The bundle is mapping class group equivariant and admits an invariant foliation. SeveralExpand
Rigidity of infinite disk patterns
Let P be a locally flnite disk pattern on the complex plane C whose combinatorics are described by the one-skeleton G of a triangulation of the open topological disk and whose dihedral angles areExpand
The virtual cohomological dimension of the mapping class group of an orientable surface
Let F = F ~ r be the mapping class group of a surface F of genus g with s punctures and r boundary components. The purpose of this paper is to establish cohomology properties of F parallel to thoseExpand
Euclidean decompositions of noncompact hyperbolic manifolds
On introduit une methode pour diviser une variete hyperbolique non compacte de volume fini en morceaux euclidiens canoniques
Combinatorial optimization in geometry
  • Igor Rivin
  • Mathematics, Physics
  • Adv. Appl. Math.
  • 2003
TLDR
The basic objects studied are the canonical Delaunay triangulations associated to the aforementioned Euclidean structures and the basic tools, in addition to the results of Rivin, Ann. Expand
Linear Programming and Extensions.
Linear programming and extensions
TLDR
Formulation skills for problems as a deterministic linear mathematical model, application of software to solve the problems and extensive sensitivity analysis to answer “what if” questions. Expand
...
1
2
3
...