On extensions of Minkowski's theorem on successive minima
Metric Geometry
2014-05-21 v1 Combinatorics
Abstract
Minkowski's 2nd theorem in the Geometry of Numbers provides optimal upper and lower bounds for the volume of a -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.
Keywords
Cite
@article{arxiv.1405.4993,
title = {On extensions of Minkowski's theorem on successive minima},
author = {Martin Henk and Matthias Henze and María A. Hernández Cifre},
journal= {arXiv preprint arXiv:1405.4993},
year = {2014}
}
Comments
18 pages