On a strong version of the Kepler conjecture
Metric Geometry
2013-02-13 v4 Optimization and Control
Abstract
We raise and investigate the following problem that one can regard as a very close relative of the densest sphere packing problem. If the Euclidean 3-space is partitioned into convex cells each containing a unit ball, how should the shapes of the cells be designed to minimize the average surface area of the cells? In particular, we prove that the average surface area in question is always at least 13.8564... .
Keywords
Cite
@article{arxiv.1111.3092,
title = {On a strong version of the Kepler conjecture},
author = {Karoly Bezdek},
journal= {arXiv preprint arXiv:1111.3092},
year = {2013}
}
Comments
9 pages