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From dual bodies to the Kneser-Poulsen conjecture Bezdek, Karoly


The Kneser--Poulsen Conjecture states that if the centers of a family of N congruent balls in Euclidean d-space is contracted, then the volume of the intersection does not decrease. A uniform contraction is a contraction where all the pairwise distances in the first set of centers are larger than all the pairwise distances in the second set of centers. We prove the Kneser-Poulsen conjecture for uniform contractions whenever N is sufficiently large (depending only on d) in Euclidean, spherical as well as hyperbolic d-space for all d>1.

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