Successive minima, intrinsic volumes, and lattice determinants

DOI10.1007/BF02574040zbMath0818.52003OpenAlexW1997042099MaRDI QIDQ1346140

Uwe Schnell

Publication date: 20 March 1995

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131358

zbMATH Keywords

convex bodiessuccessive minimaintrinsic volumeslattice determinants

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

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• Minkowski's successive minima and the zeros of a convexity-function
• Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice
• Bounds for the lattice point enumerator
• Two isoperimetric inequalities with lattice constraints
• Lattice inequalities for convex bodies and arbitrary lattices
• An inequality relating volume, area and number of lattice points of convex sets in \(n\)-dimensional Euclidean space
• Gitterperiodische Punktmengen und Isoperimetrie
• Inequalities between successive minima and intrinsic volumes of a convex body
• On successive minima and intrinsic volumes
• Minimal Determinants and Lattice Inequalities
• Non-linear angle-sum relations for polyhedral cones and polytopes

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