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Discrete & Computational Geometry

, Volume 32, Issue 1, pp 101–106 | Cite as

The Kneser–Poulsen Conjecture for Spherical Polytopes

  • Károly Bezdek
  • Robert Connelly
Article

Abstract

If a finite set of balls of radius π/2 (hemispheres) in the unit sphere Sn is rearranged so that the distance between each pair of centers does not decrease, then the (spherical) volume of the intersection does not increase, and the (spherical) volume of the union does not decrease. This result is a spherical analog to a conjecture by Kneser (1954) and Poulsen (1955) in the case when the radii are all equal to π/2.

Keywords

Unit Sphere Spherical Analog 
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.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, T2N 1N4Canada
  2. 2.Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853USA

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