Iskander Aliev ; Martin Henk - 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) - https://doi.org/10.46298/cm.11155
Minkowski's successive minima in convex and discrete geometry

Authors: 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.


    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

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