Functionals on the spaces of convex bodies

DOI10.1007/s10114-015-4386-2zbMath1335.52028arXiv1402.3684OpenAlexW2066636799MaRDI QIDQ256413

Chuan Ming Zong

Publication date: 9 March 2016

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.3684

zbMATH Keywords

kissing numberpacking densitycovering densityHadwiger's conjecture

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Three-dimensional polytopes (52B10) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17)

Related Items

Covering functionals of cones and double cones ⋮ Covering the boundary of a convex body with its smaller homothetic copies ⋮ A Computer Approach to Determine the Densest Translative Tetrahedron Packings ⋮ Covering unit spheres and balls of normed spaces by smaller balls ⋮ Covering a convex body vs. covering the set of its extreme points ⋮ On covering functionals of convex bodies

Cites Work

• A quantitative program for Hadwiger's covering conjecture
• Covering the plane with translates of a triangle
• Metrically invariant measures on locally homogeneous spaces and hyperspaces
• Sphere packings. (Edited by John Talbot)
• The antipode construction for sphere packings
• The simultaneous packing and covering constants in the plane
• The closest packing of convex two-dimensional domains
• Research Problems in Discrete Geometry
• Measures on the space of convex bodies
• The maximum distance between two-dimensional Banach spaces.
• SIMULTANEOUS PACKING AND COVERING IN THREE–DIMENSIONAL EUCLIDEAN SPACE
• Mysteries in Packing Regular Tetrahedra
• Metric entropy and approximation
• A Note on Coverings and Packings
• Sur la densité des réseaux de domaines convexes
• A Compactness Theorem For Affine Equivalence-Classes of Convex Regions
• Inequalities between lattice packing and covering densities of centrally symmetric plane convex bodies
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