The Kneser-Poulsen conjecture says that if a finite collection of balls in the Euclidean space $E^d$ is rearranged so that the distance between each pair of centers does not get smaller, then the volume of the union of these balls also does not get smaller. In this paper, we prove that if in the initial configuration the intersection of any two balls has common points with no more than $d+1$ other balls, then the conjecture holds.
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机译：Kneser-Poulsen猜想说，如果重新排列欧几里得空间$ E ^ d $中的有限球集合，以使每对中心之间的距离不会变小，那么这些球的并集体积也不会变小。在本文中，我们证明，如果在初始配置中，任何两个球的交点具有相同的点，而其他球不超过$ d + 1 $，则该猜想成立。
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