volume 27, issue 2, P165-193 2002
DOI: 10.1007/s00454-001-0060-9
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Abstract: AbstractThis paper formalizes the local density inequality approach to getting upper bounds for sphere packing densities in R n . This approach was first suggested by L. Fejes-Tóth in 1954 as a method to prove the Kepler conjecture that the densest packing of unit spheres in R 3 has density π √ 18 , which is attained by the "cannonball packing." Local density inequalities give upper bounds for the sphere packing density formulated as an optimization problem of a nonlinear function over a compact set in a fini…

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