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Tr. Mat. Inst. Steklova, 2011, Volume 275, Pages 240–249 (Mi tm3347)  

This article is cited in 4 scientific papers (total in 4 papers)

Lattice packing and covering of convex bodies

Peter M. Gruber

Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Vienna, Austria

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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2011, 275, 229–238

Bibliographic databases:

UDC: 514.17+511.9
Received in May 2011
Language:

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, Tr. Mat. Inst. Steklova, 275, MAIK Nauka/Interperiodica, Moscow, 2011, 240–249; Proc. Steklov Inst. Math., 275 (2011), 229–238

Citation in format AMSBIB
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\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 Tr. Mat. Inst. Steklova
\yr 2011
\vol 275
\pages 240--249
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3347}
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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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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856428635}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Proc. Steklov Inst. Math., 276 (2012), 103–124  mathnet  crossref  mathscinet  isi  elib
    2. Gruber P.M., “Application of an Idea of Voronoa to Lattice Packing”, Ann. Mat. Pura Appl., 193:4 (2014), 939–959  crossref  mathscinet  zmath  isi
    3. Gruber P.M., “Normal Bundles of Convex Bodies”, Adv. Math., 254 (2014), 419–453  crossref  mathscinet  zmath  isi
    4. Gruber P.M., “Extremum properties of lattice packing and covering with circles”, Adv. Geom., 16:1 (2016), 93–110  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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