Geometry & Topology

Characterizing the Delaunay decompositions of compact hyperbolic surfaces

Gregory Leibon

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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.

Article information

Geom. Topol., Volume 6, Number 1 (2002), 361-391.

Received: 28 March 2001
Revised: 8 July 2002
Accepted: 9 July 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52C26: Circle packings and discrete conformal geometry
Secondary: 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15]

Delaunay triangulation hyperbolic polyhedra disk pattern


Leibon, Gregory. Characterizing the Delaunay decompositions of compact hyperbolic surfaces. Geom. Topol. 6 (2002), no. 1, 361--391. doi:10.2140/gt.2002.6.361.

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