Naslov
Inhomogeneous extreme forms

Autori
Dutour Sikirić, Mathieu ; Schuermann, Achill ; Vallentin, Frank

Izvornik
Annales de l institut fourier (0373-0956) 62 (2012), 6; 2227-2255

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Lattices; Delaunay polytopes; spherical t-designs; sphere packing; sphere covering; Voronoi reduction theory

Sažetak
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 the 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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