The Delaunay tessellation in hyperbolic space
Geometric Topology
2016-08-09 v3
Abstract
The Delaunay tessellation of a locally finite subset of hyperbolic space is constructed using convex hulls in Euclidean space of one higher dimension. 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.
Cite
@article{arxiv.1308.4899,
title = {The Delaunay tessellation in hyperbolic space},
author = {Jason DeBlois},
journal= {arXiv preprint arXiv:1308.4899},
year = {2016}
}
Comments
Some changes suggested by a referee, most significantly in Section 4, where in particular a figure is added