常曲率平面上的两个Kneser-Poulsen型不等式
Two Kneser--Poulsen-type Inequalities in Planes of Constant Curvature
摘要：
我们表明，周长的凸包的许多磁盘躺在双曲线或欧几里得平面，或在半球不增加时，磁盘重新安排，使它们的中心之间的距离不增加。这推广了V.N.在欧氏平面上证明的关于压缩下有限集的凸包周长单调性的定理。苏达科夫河Alexander，V. Capoyleas and J. Pach.我们还证明了在这样的压缩重排后，在双曲平面中的多个圆盘的相交面积不会减小。后一种说法的欧几里德类比由K. Bezdek和R.康奈利这两个定理证明了一个适当的适应最近发表的方法I。Gorbovickis。
英文摘要：
We show that the perimeter of the convex hull of finitely many disks lying in the hyperbolic or Euclidean plane, or in a hemisphere does not increase when the disks are rearranged so that the distances between their centers do not increase. This generalizes the theorem on the monotonicity of the perimeter of the convex hull of a finite set under contractions, proved in the Euclidean plane by V. N. Sudakov, R. Alexander, V. Capoyleas and J. Pach. We also prove that the area of the intersection of finitely many disks in the hyperbolic plane does not decrease after such a contractive rearrangement. The Euclidean analogue of the latter statement was proved by K. Bezdek and R. Connelly. Both theorems are proved by a suitable adaptation of a recently published method of I. Gorbovickis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
