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Selected Proofs on the Kneser–Poulsen Conjecture

  • Károly Bezdek
Chapter
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

First, recall the following underlying system of (truncated) Voronoi cells. For a given point configuration p = (p1, p2, …, p N) in \(\mathbb{E}^d\) and radii r 1, r 2, …, r N consider the following sets,
$$\mathbf{V}_{i} = \{{\rm x} \in \mathbb{E}^d |\,\mbox{for all}\,j, \|{\rm x} - \mathbf{p}_i\|^2 - r_{i}^{2} \leq \|{\rm x} - \mathbf{p}_{j}\|^2 - r_{j}^{2}\},$$
$$\mathbf{V}^{i} = \{{\rm x} \in \mathbb{E}^d |\,\mbox{for all}\,j, \|{\rm x} - \mathbf{p}_i\|^2 - r_{i}^{2} \geq \|{\rm x} - \mathbf{p}_{j}\|^2 - r_{j}^{2}\}.$$

Keywords

Dihedral Angle Voronoi Cell Spherical Distance Convex Corner Nite Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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