Minkowski's successive minima in convex and discrete geometry

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.

Accepted for publication in Communications in Mathematics

References in corpus (4)

• Logarithmic bounds for isoperimetry and slices of convex sets
• Interpolating between volume and lattice point enumerator with successive minima
• Volume Product
• New bounds in the discrete analogue of Minkowski's second theorem

Cited by in corpus (1)

• Euclidean lattices: theory and applications