Nalazite se na CroRIS probnoj okolini. Ovdje evidentirani podaci neće biti pohranjeni u Informacijskom sustavu znanosti RH. Ako je ovo greška, CroRIS produkcijskoj okolini moguće je pristupi putem poveznice www.croris.hr
izvor podataka: crosbi

Inhomogeneous extreme forms (CROSBI ID 173603)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dutour Sikirić, Mathieu ; Schuermann, Achill ; Vallentin, Frank Inhomogeneous extreme forms // Annales de l institut fourier, 62 (2012), 6; 2227-2255. doi: 10.5802/aif.2748

Podaci o odgovornosti

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

engleski

Inhomogeneous extreme forms

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.

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

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

Podaci o izdanju

62 (6)

2012.

2227-2255

objavljeno

0373-0956

10.5802/aif.2748

Povezanost rada

Matematika

Poveznice
Indeksiranost