2 papers
math.MG2001
Improving Rogers' upper bound for the density of unit ball packings via estimating the surface area of Voronoi cells from below in Euclidean d-space for all d>7
Karoly Bezdek
The sphere packing problem asks for the densest packing of unit balls in d-dimensional Euclidean space. This problem has its roots in geometry, number theory and it is part of Hilb…
math.MG2001
Pushing disks apart - The Kneser-Poulsen conjecture in the plane
Károly Bezdek, Robert Connelly
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…