Inhomogeneous extreme forms

Details Inhomogeneous extreme forms Inhomogeneous extreme forms

2010-08-27

arxiv.org/abs/1008.4751v2

Mathematics

Number Theory

22 pages, revision based on suggestions by referee, accepted in Annales de l'Institut Fourier

Scientific paper

G.F. Voronoi (1868-1908) wrote two memoirs in which he describes two reduction theories for lattices, well-suited for sphere packing and covering problems. In his first memoir a characterization of locally most economic packings is given, but a corresponding result for coverings has been missing. In this paper we bridge the two classical memoirs. By looking at the covering problem from a different perspective, we discover the missing analogue. Instead of trying to find lattices giving economical coverings we consider lattices giving, at least locally, very uneconomical ones. We classify local covering maxima up to dimension 6 and prove their existence in all dimensions beyond. New phenomena arise: Many highly symmetric lattices turn out to give uneconomical coverings; the covering density function is not a topological Morse function. Both phenomena are in sharp contrast to the packing problem.

Affiliated with

Also associated with

No associations

Rating

Inhomogeneous extreme forms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inhomogeneous extreme forms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inhomogeneous extreme forms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331919