Lattice packing and covering of convex bodies

DOI10.1134/S0081543811080165zbMath1301.52033MaRDI QIDQ741181

Peter M. Gruber

Publication date: 10 September 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

densitykissing number problemlattice packings and coverings balls

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07)

Related Items (3)

Normal bundles of convex bodies ⋮ Application of an idea of Voronoĭ to lattice packing ⋮ Application of an idea of Voronoĭ to lattice zeta functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• John and Loewner ellipsoids
• Computational approaches to lattice packing and covering problems
• A lower bound on packing density
• Minimal ellipsoids and their duals
• Sur un problème de dualité lié aux sphères en géométrie des nombres. (On a duality problem related to spheres in geometry of numbers)
• Riemann surfaces with shortest geodesic of maximal length
• Systoles on Riemann surfaces
• Distributing many points on a sphere
• The minimum values of positive quadratic forms in six, seven and eight variables
• Densest lattice packings of 3-polytopes.
• Application of an idea of Voronoĭ to John type problems
• An arithmetic proof of John's ellipsoid theorem
• Minima of Epstein's zeta function and heights of flat tori
• Voronoĭ type criteria for lattice coverings with balls
• Uniqueness of lattice packings and coverings of extreme density
• Classification of eight-dimensional perfect forms
• Spherical designs and zeta functions of lattices
• Geometry of Riemann surfaces based on closed geodesics
• Hexagonal Economic Regions Solve the Location Problem
• Perfect Non-Extremal Riemann Surfaces
• The densest lattice in twenty-four dimensions
• Sur La Classification Des Réseaux Eutactiques
• Convex and Discrete Geometry
• The star number of coverings of space with convex bodies
• Extreme coverings ofn-space by spheres
• Sphere Packings and Error-Correcting Codes
• The Number of Circles Covering a Set
• Two Remarks On Extreme Forms
• On the geometry of numbers

This page was built for publication: Lattice packing and covering of convex bodies