Application of an idea of Voronoĭ to lattice packing
type: Item
instance of: scholarly article
title: Application of an idea of Voronoĭ to lattice packing
zbMATH Open document ID: 1297.05047
author: Peter M. Gruber
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2014-09-11T00:00:00Z
review text: The famous result of Voronoĭ states that a lattice packing of balls has locally maximum density if and only if it is eutactic and perfect. As a generalization, for any smooth convex ball \(c\) concepts of \(C\)-semi-eutaxy, \(C\)-eutaxy, and \(C\)-perfection are intriduced. These conceptions are connected with semi-stationarity, stationarity, and local ultra-maximality of lattice packing density for \(C\). For example, it is proved that the packing of \(C\) by the lattice \(L\) has local ultra-maximum at \(L\) if and only if \(L\) is eutactic and perfect with respect to \(C\). Similar results also proved for the product of packing densities of smooth convex body \(C\) and its polar body \(C^*\).
Mathematics Subject Classification ID: 05B40
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11H31
Mathematics Subject Classification ID: 11H55
Mathematics Subject Classification ID: 52C07
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 6342886
zbMATH Keywords: Voronoĭ-type result
zbMATH Keywords: lattice packing of balls
zbMATH Keywords: lattice packing of convex bodies
zbMATH Keywords: maximum density
zbMATH Keywords: maximum lattice
zbMATH Keywords: perfect lattice
zbMATH Keywords: eutactic lattice
reviewed by: Anton Shutov
MaRDI profile type: Publication
full work available at URL: s10231-012-0308-4
OpenAlex ID: W2095364002
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DOI: 10.1007/S10231-012-0308-4
description: scientific article; zbMATH DE number 6342886