On extensions of Minkowski's theorem on successive minima

2014/05/20 by Henk, Martin, Henze, Matthias, Cifre, María A. Hernández
#52A20 #52A40 #52B11 #52C07 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1405.4993

Abstract

Minkowski's 2nd theorem in the Geometry of Numbers provides optimal upper and lower bounds for the volume of a o-symmetric convex body in terms of its successive minima. In this paper we study extensions of this theorem from two different points of view: either relaxing the symmetry condition, assuming that the centroid of the set lies at the origin, or replacing the volume functional by the surface area.

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