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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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IMPACT FACTOR 2016: 0.755
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1435-5337
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Volume 28, Issue 2

Issues

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

Abstract

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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[1]
Sören Lennart Berg and Martin Henk
SIAM Journal on Discrete Mathematics, 2016, Volume 30, Number 2, Page 1148

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