On a strong version of the Kepler conjecture

Details On a strong version of the Kepler conjecture On a strong version of the Kepler conjecture

2011-11-14

arxiv.org/abs/1111.3092v4

Mathematics

Metric Geometry

9 pages

Scientific paper

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... .

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