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. 
@article{TRSPY_2011_275_a10,
     author = {K\'aroly Bezdek},
     title = {The illumination conjecture for spindle convex bodies},
     journal = {Informatics and Automation},
     pages = {181--187},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a10/}
}
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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/