| Abstract: | In this note, first, we give a very short new proof of the theorem which yields a lower bound for the surface area of Voronoi
cells of unit ball packings in E
d
and implies Rogers' upper bound for the density of unit ball packings in E
d
for all d ≥ 2. Second we sharpen locally a classical result of Gauss by finding the locally smallest surface area Voronoi cells of
lattice unit ball packings in E
3.
This revised version was published online in August 2006 with corrections to the Cover Date. |
