The Delaunay tessellation in hyperbolic space

被引：6
作者：
Deblois, Jason [1 ]
机构：
[1] Univ Pittsburgh, Dept Math, 301 Thackeray Hall, Pittsburgh, PA 15260 USA
来源：
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 2018年 / 164卷 / 01期
关键词：
MANIFOLDS; SURFACES;
D O I：
10.1017/S0305004116000827
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Delaunay tessellation of a locally finite subset of the hyperbolic space H-n 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.
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页码：15 / 46
页数：32
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