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The Delaunay tessellation in hyperbolic space

Published online by Cambridge University Press:  27 September 2016

JASON DEBLOIS
JASON DEBLOIS*
Affiliation:
Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall Pittsburgh, PA 15260 e-mail: jdeblois@pitt.edu
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Abstract

The Delaunay tessellation of a locally finite subset of the hyperbolic space ℍn is constructed via convex hulls in ℝn+1. For finite and lattice-invariant sets it is proven to be a polyhedral decomposition, and versions (necessarily modified from the Euclidean setting) of the empty circumspheres condition and geometric duality with the Voronoi tessellation are proved. Some pathological examples of infinite, non lattice-invariant sets are exhibited.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 164 , Issue 1 , January 2018 , pp. 15 - 46
Copyright
Copyright © Cambridge Philosophical Society 2016 

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References

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