Geodesic
The illumination conjecture for spindle convex bodies
Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 181-187.

Voir la notice de l'article provenant de la source Math-Net.Ru

A subset of the $d$-dimensional Euclidean space having nonempty interior is called a spindle convex body if it is the intersection of (finitely or infinitely many) congruent $d$-dimensional closed balls. A spindle convex body is called a “fat” one if it contains the centers of its generating balls. The main result of this paper is a proof of the illumination conjecture for “fat” spindle convex bodies in dimensions greater than or equal to 15. 
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     author = {K\'aroly Bezdek},
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Károly Bezdek. The illumination conjecture for spindle convex bodies. Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 181-187. http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a10/

[1] Aigner M., Ziegler G.M., Proofs from The Book, 4th ed., Springer, Berlin, 2010 | MR

[2] Bezdek K., “The illumination conjecture and its extensions”, Period. math. Hung., 53:1–2 (2006), 59–69 | DOI | MR | Zbl

[3] Bezdek K., Lángi Zs., Naszódi M., Papez P., “Ball-polyhedra”, Discr. and Comput. Geom., 38:2 (2007), 201–230 | DOI | MR | Zbl

[4] Bezdek K., Kiss Gy., “On the X-ray number of almost smooth convex bodies and of convex bodies of constant width”, Can. Math. Bull., 52:3 (2009), 342–348 | DOI | MR | Zbl

[5] Boltyanskii V.G., “Zadacha ob osveschenii granitsy vypuklogo tela”, Izv. Mold. fil. AN SSSR, 1960, no. 10, 77–84

[6] Boltyanskii V.G., Gokhberg I.Ts., Razbienie figur na menshie chasti, Nauka, M., 1971

[7] Dekster B.V., “Completeness and constant width in spherical and hyperbolic spaces”, Acta math. Hung., 67:4 (1995), 289–300 | DOI | MR | Zbl

[8] Dekster B.V., “The Jung theorem for spherical and hyperbolic spaces”, Acta math. Hung., 67:4 (1995), 315–331 | DOI | MR | Zbl

[9] Fowler P.W., Tarnai T., “Transition from spherical circle packing to covering: Geometrical analogues of chemical isomerization”, Proc. Roy. Soc. London A, 452 (1996), 2043–2064 | DOI | MR | Zbl

[10] Hadwiger H., “Ungelöste Probleme. Nr. 38”, Elem. Math., 15 (1960), 130–131 | MR

[11] Kahn J., Kalai G., “A counterexample to Borsuk's conjecture”, Bull. Amer. Math. Soc., 29:1 (1993), 60–62 | DOI | MR | Zbl

[12] Lassak M., “Covering the boundary of a convex set by tiles”, Proc. Amer. Math. Soc., 104:1 (1988), 269–272 | DOI | MR | Zbl

[13] Meissner E., “Über Punktmengen konstanter Breite”, Vierteljahresschr. naturforsch. Ges. Zürich, 56 (1911), 42–50 | Zbl

[14] Schramm O., “Illuminating sets of constant width”, Mathematika, 35:2 (1988), 180–189 | DOI | MR | Zbl