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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 28, Issue 2


Variations of Minkowski's theorem on successive minima

Martin Henk / Matthias Henze / María A. Hernández Cifre
Published Online: 2015-01-10 | DOI: https://doi.org/10.1515/forum-2014-0093


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

Keywords: Minkowski's second theorem; successive minima; centroid; volume; surface area; lattice surface area; convex body; rational polytope

MSC: 52A40; 52A20; 52B11; 52C07

About the article

Received: 2014-05-23

Revised: 2014-07-17

Published Online: 2015-01-10

Published in Print: 2016-03-01

Funding Source: MINECO-FEDER

Award identifier / Grant number: MTM2012-34037

Funding Source: DFG

Award identifier / Grant number: He 2272/4-1

Funding Source: DFG

Award identifier / Grant number: RO 2338/5-1

Citation Information: Forum Mathematicum, Volume 28, Issue 2, Pages 311–325, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0093.

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