volume 32, issue 1, P101-106 2004
DOI: 10.1007/s00454-004-0831-1
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Abstract: Abstract. If a finite set of balls of radius π/2 (hemispheres) in the unit sphere S n 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.

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