Abstract:
The aim of this article is twofold. First, to indicate briefly major problems and developments dealing with lattice packings and coverings of balls and convex bodies. Second, to survey more recent results on uniqueness of lattice packings and coverings of extreme density, on characterization of local minima and maxima of the density and on estimates of the kissing number. Emphasis is on results in general dimensions.
Citation:
Peter M. Gruber, “Lattice packing and covering of convex bodies”, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth, Trudy Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 240–249; Proc. Steklov Inst. Math., 275 (2011), 229–238
\Bibitem{Gru11}
\by Peter~M.~Gruber
\paper Lattice packing and covering of convex bodies
\inbook Classical and modern mathematics in the wake of Boris Nikolaevich Delone
\bookinfo Collected papers. In commemoration of the 120th anniversary of Boris Nikolaevich Delone's birth
\serial Trudy Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 240--249
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 275
\pages 229--238
\crossref{https://doi.org/10.1134/S0081543811080165}
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