On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width
Printed: Sep 2009
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 $6$.
almost smooth convex body, convex body of constant width, weakly neighbourly antipodal convex polytope, Illumination Conjecture, X-ray number, X-ray Conjecture
52A20 - Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
52A37 - Other problems of combinatorial convexity
52C17 - Packing and covering in $n$ dimensions [See also 05B40, 11H31]
52C35 - Arrangements of points, flats, hyperplanes [See also 32S22]