On the Hadwiger covering problem in low dimensions

DOI10.1007/s00022-020-00554-3zbMath1451.52003arXiv1811.08962OpenAlexW3088569456MaRDI QIDQ2210788

Andriy Prymak, Varvara Shepelska

Publication date: 8 November 2020

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08962

zbMATH Keywords

convex bodycovering numberillumination numberillumination problemcovering by smaller homothetic copies4-cube

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Other problems of combinatorial convexity (52A37) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (5)

Improved bounds for Hadwiger's covering problem via thin-shell estimates ⋮ Borsuk's partition problem in ℓₚ⁴ ⋮ A New Bound for Hadwiger’s Covering Problem in \(\boldsymbol{\mathbb{E}}^3\) ⋮ Spherical coverings and X-raying convex bodies of constant width ⋮ Illuminating spiky balls and cap bodies

Cites Work

• The difference body of a convex body
• An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
• The geometry of homothetic covering and illumination
• A note on coverings
• Covering the Boundary of a Convex Set by Tiles

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