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Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces

Part of: General convexity Geometric probability and stochastic geometry

Published online by Cambridge University Press:  19 February 2016

Yukinao Isokawa
Yukinao Isokawa*
Affiliation:
Kagoshima University
*
∗ Postal address: Faculty of Education, Kagoshima University, Kagoshima, Japan. Email address: isokawa@edu.kagoshima-u.ac.jp
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Abstract

We study Poisson-Voronoi tessellations in three-dimensional hyperbolic spaces, and give explicit expressions for mean surface area, mean perimeter length, and mean number of vertices of their cells. Furthermore we compare these mean characteristics with those for Poisson-Voronoi tessellations in three-dimensional Euclidean spaces. It is shown that, as the absolute value of the curvature of hyperbolic spaces increases from zero to infinity, these mean characteristics increase monotonically from those for the Euclidean case to infinity.

Keywords

Random tessellationVoronoi tessellationmean characteristicshyperbolic space

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 52A22: Random convex sets and integral geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 3 , September 2000 , pp. 648 - 662
Copyright
Copyright © Applied Probability Trust 2000 

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