1 4 A ug 2 00 1 PUSHING DISKS APART - THE KNESER - POULSEN CONJECTURE IN THE PLANE
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چکیده
We give a proof of the planar case of a longstanding conjecture of Kneser (1955) and Poulsen (1954). In fact, we prove more by showing that if a finite set of disks in the plane is rearranged so that the distance between each pair of centers does not decrease, then the area of the union does not decrease, and the area of the intersection does not increase.
منابع مشابه
On the Perimeter of the Intersection of Congruent Disks
Almost 20 years ago, R. Alexander conjectured that, under an arbitrary contraction of the center points of finitely many congruent disks in the plane, the perimeter of the intersection of the disks cannot decrease. Even today it does not seem to lie within reach. What makes this problem even more important is the common belief that it would give a sharpening of the well-known Kneser-Poulsen con...
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تاریخ انتشار 2002