Successive minima, intrinsic volumes, and lattice determinants
type: Item
instance of: scholarly article
title: Successive minima, intrinsic volumes, and lattice determinants
zbMATH Open document ID: 0818.52003
DOI: 10.1007/BF02574040
author: Uwe Schnell
published in: Discrete \& Computational Geometry
publication date: 1995-03-20T00:00:00Z
full work available at URL: https://eudml.org/doc/131358
review text: For arbitrary lattices in euclidean \(d\)-space \(E^ d\) the author considers inequalities between the successive minima \(\lambda_ i\) and the intrinsic volumes \(V_ i\) of \(O\)-symmetric convex bodies, i.e. analogues of Minkowski's second fundamental theorem in Geometry of Numbers. Clearly the \(V_ i\) (except the volume) are not equi-affine invariant, so suitable functionals of the lattice have to be introduced, which lead to a general series of inequalities between the \(\lambda_ i\), the \(V_ i\) and suitable lattice constants.
Mathematics Subject Classification ID: 52A20
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A38
Mathematics Subject Classification ID: 52C07
zbMATH DE Number: 735347
zbMATH Keywords: lattice determinants
zbMATH Keywords: successive minima
zbMATH Keywords: intrinsic volumes
zbMATH Keywords: convex bodies
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
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OpenAlex ID: W1997042099
description: scientific article; zbMATH DE number 735347