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1. CMB 2009 (vol 52 pp. 342)
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On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width The X-ray numbers of some classes of convex bodies are investigated.
In particular, we give a proof of the X-ray Conjecture as well as
of the Illumination Conjecture for almost smooth convex bodies
of any dimension and for convex bodies of constant width of
dimensions $3$, $4$, $5$ and $6$.
Keywords:almost smooth convex body, convex body of constant width, weakly neighbourly antipodal convex polytope, Illumination Conjecture, X-ray number, X-ray Conjecture Categories:52A20, 52A37, 52C17, 52C35 |