Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\)
type: Item
instance of: scholarly article
title: Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\)
zbMATH Open document ID: 0824.52011
DOI: 10.1007/BF02574039
published in: Discrete \& Computational Geometry
publication date: 1995-11-12T00:00:00Z
full work available at URL: https://eudml.org/doc/131357
review text: For a lattice \(L\) and an \(o\)-symmetric convex body in \(\mathbb{R}^ n\) let \(\lambda_ i (L, U)\) denote Minkowski's successive minima. Upper bounds are established for \(\lambda_ i (L, U) \lambda_{n-i +1} (L^*, V)\) where \(L^*\) is the dual lattice of \(L\) and \(U\), \(V\) are unit balls of the spaces \(l^ n_ p\), \(1\leq p\leq \infty\). The upper bounds are compared with known lower bounds.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 735346
zbMATH Keywords: successive minima
zbMATH Keywords: lattice
zbMATH Keywords: polar body
author: Wojciech Banaszczyk
reviewed by: Erhard Heil
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 735346