Bodies of Constant Width in Analysis

2019 ◽  
pp. 299-320
Author(s):  
Horst Martini ◽  
Luis Montejano ◽  
Déborah Oliveros
Keyword(s):  
Constant Width ◽  
Bodies Of Constant Width

scholarly journals Spherical bodies of constant width

2018 ◽  
Vol 92 (4) ◽  
pp. 627-640 ◽  
Author(s):  
Marek Lassak ◽  
Michał Musielak
Keyword(s):  
Constant Width ◽  
Bodies Of Constant Width

Bodies of Constant Width in Art, Design, and Engineering

2019 ◽  
pp. 425-443
Author(s):  
Horst Martini ◽  
Luis Montejano ◽  
Déborah Oliveros
Keyword(s):  
Constant Width ◽  
Art Design ◽  
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.

Bodies of Constant Width in Differential Geometry

2019 ◽  
pp. 247-277
Author(s):  
Horst Martini ◽  
Luis Montejano ◽  
Déborah Oliveros
Keyword(s):  
Differential Geometry ◽  
Constant Width ◽  
Bodies Of Constant Width

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
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