Minkowski’s successive minima in convex and discrete geometry

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 and Henk, Martin 2023. Minkowski’s successive minima in convex and discrete geometry. Communications in Mathematics 31 (2) , 3. 10.46298/cm.11155

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Abstract

In this short survey we want to present some of the impact of Minkowski’s successive minima within Convex and Discrete Geometry. Originally related to the volume of an o-symmetric convex body, we point out relations of the successive minima to other functionals, as e.g., the lattice point enumerator or the intrinsic volumes and we present some old and new conjectures about them. Additionally, we discuss an application of successive minima to a version of Siegel’s lemma.

Item Type:	Article
Date Type:	Published Online
Status:	Published
Schools:	Mathematics
Publisher:	EPIsciences
ISSN:	1804-1388
Date of First Compliant Deposit:	16 May 2023
Date of Acceptance:	27 April 2023
Last Modified:	19 Dec 2023 14:57
URI:	https://orca.cardiff.ac.uk/id/eprint/159308

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