scholarly journals Spherical coverings and X-raying convex bodies of constant width

2021 ◽  
pp. 1-7
Author(s):  
Andriy Bondarenko ◽  
Andriy Prymak ◽  
Danylo Radchenko
Keyword(s):  
Constant Width ◽  
Convex Bodies ◽  
Bodies Of Constant Width

scholarly journals THE ROSENTHAL–SZASZ INEQUALITY FOR NORMED PLANES

2018 ◽  
Vol 99 (1) ◽  
pp. 130-136
Author(s):  
VITOR BALESTRO ◽  
HORST MARTINI
Keyword(s):  
Differential Geometry ◽  
Upper Bound ◽  
Constant Width ◽  
Convex Bodies ◽  
Euclidean Case ◽  
Planar Convex ◽  
Arbitrary Norms ◽  
Bodies Of Constant Width ◽  
Curves Of Constant Width ◽  
Normed Planes

We study the classical Rosenthal–Szasz inequality for a plane whose geometry is determined by a norm. This inequality states that the bodies of constant width have the largest perimeter among all planar convex bodies of given diameter. In the case where the unit circle of the norm is given by a Radon curve, we obtain an inequality which is completely analogous to the Euclidean case. For arbitrary norms we obtain an upper bound for the perimeter calculated in the anti-norm, yielding an analogous characterisation of all curves of constant width. To derive these results, we use methods from the differential geometry of curves in normed planes.

scholarly journals On convex bodies of constant width

2006 ◽  
Vol 153 (11) ◽  
pp. 1699-1704 ◽  
Author(s):  
L.E. Bazylevych ◽  
M.M. Zarichnyi
Keyword(s):  
Constant Width ◽  
Convex Bodies ◽  
Bodies Of Constant Width

scholarly journals On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width

2009 ◽  
Vol 52 (3) ◽  
pp. 342-348 ◽  
Author(s):  
K. Bezdek ◽  
Gy. Kiss
Keyword(s):  
Constant Width ◽  
Convex Bodies ◽  
Smooth Convex ◽  
X Ray ◽  
Bodies Of Constant Width

AbstractThe 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.

scholarly journals Hyperspaces of convex bodies of constant width

2015 ◽  
Vol 196 ◽  
pp. 347-361 ◽  
Author(s):  
Sergey A. Antonyan ◽  
Natalia Jonard-Pérez ◽  
Saúl Juárez-Ordóñez
Keyword(s):  
Constant Width ◽  
Convex Bodies ◽  
Bodies Of Constant Width
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