Perfect, strongly eutactic lattices are periodic extreme |
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Authors: | Achill Schürmann |
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Institution: | Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands |
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Abstract: | We introduce a parameter space for periodic point sets, given as unions of m translates of point lattices. In it we investigate the behavior of the sphere packing density function and derive sufficient conditions for local optimality. Using these criteria we prove that perfect, strongly eutactic lattices cannot be locally improved to yield a periodic sphere packing with greater density. This applies in particular to the densest known lattice sphere packings in dimension d?8 and d=24. |
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Keywords: | 52C17 11H55 |
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