The Kneser–Poulsen Conjecture for Spherical Polytopes

Authors:
Károly Bezdek;Robert Connelly
Affiliations:
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, Alberta, T2N 1N4, Canada;Department of Mathematics, Malott Hall, Cornell University, Ithaca, NY 14853, USA
Venue:
Discrete & Computational Geometry
Year:
2004

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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.