The Kneser-Poulsen conjecture for spherical polytopes
The authors prove the following result and some related statements: If a finite set of balls of radius \(\frac{\pi}{2}\) in the unit sphere \(S^n\) of Euclidean \((n+1)\)-space 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 can be considered as a spherical analogue of the Kneser-Poulsen conjecture for radii all equal to \(\frac{\pi}{2}\).
scientific article; zbMATH DE number 2123183