This is an announcement for the paper "In which dimensions is the ball relatively worst packing?" by Yoav Kallus and Fedor Nazarov.

Abstract: It was conjectured by Ulam that the ball has the lowest optimal lattice packing density out of all convex, origin-symmetric three-dimensional solids. We affirm a local version of this conjecture: the ball has a lower optimal lattice packing than any body of sufficiently small asphericity in three dimensions. We also show that in dimensions 4, 5, 6, 7, 8, and 24 there are bodies of arbitrarily small asphericity that pack worse than balls.

Archive classification: math.MG cond-mat.soft math.FA

Remarks: 15 pages, 1 figure

Submitted from: ykallus@princeton.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1212.2551

or

http://arXiv.org/abs/1212.2551