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Variations of Minkowski's theorem on successive minima
-
Martin Henk
,
Matthias Henze
Veröffentlicht/Copyright:
10. Januar 2015
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
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
Received: 2014-5-23
Revised: 2014-7-17
Published Online: 2015-1-10
Published in Print: 2016-3-1
© 2016 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
Schlagwörter für diesen Artikel
Minkowski's second theorem;
successive minima;
centroid;
volume;
surface area;
lattice surface area;
convex body;
rational polytope
Artikel in diesem Heft
- Frontmatter
- Ring class invariants over imaginary quadratic fields
- The structure of p-local compact groups of rank 1
- Sampling and interpolation on some nilpotent Lie groups
- Topology of moduli spaces of free group representations in real reductive groups
- Finite symmetries of S4
- Variations of Minkowski's theorem on successive minima
- A one-relator group with long lower central series
- On transfinite nilpotence of the Vogel–Levine localization
- Time inhomogeneous generalized Mehler semigroups and skew convolution equations
- Specifying the Auslander–Reiten translation for complexes of modules
- Second order elliptic operators with diffusion coefficients growing as |x|α at infinity
- On the fourth derivative test for exponential sums
