Iskander Aliev ; Martin Henk
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Minkowski's successive minima in convex and discrete geometry
cm:11155 -
Communications in Mathematics,
May 18, 2023,
Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications)
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https://doi.org/10.46298/cm.11155Minkowski's successive minima in convex and discrete geometryArticle
Authors: Iskander Aliev ; Martin Henk
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Iskander Aliev;Martin Henk
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.
Comment: Accepted for publication in Communications in Mathematics
Volume: Volume 31 (2023), Issue 2 (Special issue: Euclidean lattices: theory and applications)
Published on: May 18, 2023
Accepted on: April 27, 2023
Submitted on: April 4, 2023
Keywords: Mathematics - Metric Geometry, 52-02