Illuminating spindle convex bodies and minimizing the volume of spherical sets of constant width

DOI10.1007/s00454-011-9369-1zbMath1246.52006arXiv1102.1194OpenAlexW3098595532MaRDI QIDQ664363

Károly Bezdek

Publication date: 1 March 2012

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

Full work available at URL: https://arxiv.org/abs/1102.1194

zbMATH Keywords

Boltyanski-Hadwiger illumination conjecture(fat) spindle convex bodiesconstant width sets in spherical spaceconvex bodies of constant width in spherical spaceGauss (resp., normal) images of facesillumination by random directionsillumination conjecturespindle convex hull

Mathematics Subject Classification ID

Convex sets in (3) dimensions (including convex surfaces) (52A15) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items

Improved bounds for Hadwiger's covering problem via thin-shell estimates ⋮ Ball convex bodies in Minkowski spaces ⋮ Spherical Geometry—A Survey on Width and Thickness of Convex Bodies ⋮ Rogers-Shephard inequality for log-concave functions ⋮ On a strengthening of the Blaschke-Leichtweiss theorem ⋮ On the multiple illumination numbers of convex bodies ⋮ HILBERT TRANSFORMS ALONG LIPSCHITZ DIRECTION FIELDS: A LACUNARY MODEL ⋮ On variational problems related to steepest descent curves and self-dual convex sets on the sphere ⋮ Cube is a strict local maximizer for the illumination number ⋮ On covering functionals of convex bodies ⋮ Illuminating spiky balls and cap bodies

Cites Work

• Unnamed Item
• The difference body of a convex body
• Combinatorial problems on the illumination of convex bodies
• An estimate for the problem of illumination of the boundary of a convex body in \(E^3\)
• Solution of the illumination problem for three-dimensional convex bodies.
• Completeness and constant width in spherical and hyperbolic spaces
• The Jung theorem for spherical and hyperbolic spaces
• Analytic parametrization of three-dimensional bodies of constant width
• Ball-polyhedra
• The illumination conjecture and its extensions
• Covering spheres with spheres
• Transition from spherical circle packing to covering: geometrical analogues of chemical isomerization
• A counterexample to Borsuk’s conjecture
• On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width
• Illuminating sets of constant width
• Covering the Boundary of a Convex Set by Tiles
• The star number of coverings of space with convex bodies
• Covering space with convex bodies
• Steiner’s formulae on a general 𝑆ⁿ⁺¹
• On Parallel Hypersurfaces in the Elliptic and Hyperbolic n-Dimensional Space
• Proofs from THE BOOK