Pushing disks apart - The Kneser-Poulsen conjecture in the plane

Details Pushing disks apart - The Kneser-Poulsen conjecture in the plane Pushing disks apart - The Kneser-Poulsen conjecture in the plane

2001-08-14

arxiv.org/abs/math/0108098v1

Mathematics

Metric Geometry

12 pages, 3 figures, AMS TeX

Scientific paper

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.

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