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

2002/01/27 by Károly Bezdek, Robert Connelly · 65 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Point processes and geometric inequalities #Stochastic processes and statistical mechanics #Conjecture #Plane (geometry) #Mathematics #Geometry #Computer science #Combinatorics

paper · doi:10.1515/crll.2002.101

published in Journal für die reine und angewandte Mathematik (Crelles Journal) 2002(553) (De Gruyter)

openalex publication_date 2002/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a proof of the planar case of a longstanding conjecture of Kneser (1955) andPoulsen (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.

Citations

• The union of balls and its dual shape

Cited by

• Hugo Hadwiger [wikipedia]