Covering convex bodies by cylinders and lattice points by flats

DOI10.1007/s12220-008-9063-6zbMath1175.52008arXiv0903.4842OpenAlexW2067891397MaRDI QIDQ836226

Károly Bezdek, Alexander E. Litvak

Publication date: 31 August 2009

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.4842

zbMATH Keywords

convex bodyBanach-Mazur distancecovering by cylinderscovering lattice points by flats

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Geometry and structure of normed linear spaces (46B20) Local theory of Banach spaces (46B07) Inequalities and extremum problems involving convexity in convex geometry (52A40) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items

Packing convex bodies by cylinders

Cites Work

• Covering minima and lattice-point-free convex bodies
• Projections onto Hilbertian subspaces of Banach spaces
• Holomorphic semi-groups and the geometry of Banach spaces
• Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\). II: Application of \(K\)-convexity
• Distances between non-symmetric convex bodies and the \(MM^*\)-estimate
• Convex Bodies Associated with a Given Convex Body
• Ellipsoids defined by Banach ideal norms
• The Flatness Theorem for Nonsymmetric Convex Bodies via the Local Theory of Banach Spaces
• Inequalities for the Difference Body of a Convex Body
• A Solution of the "Plank Problem"
• Covering lattice points by subspaces
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