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math.MG2014
Typical curvature behaviour of bodies of constant width
Imre Barany, rolf Schneider
It is known that an -dimensional convex body which is typical in the sense of Baire category, shows a simple, but highly non-intuitive curvature behaviour: at almost all of its…
math.MG2014
Affine diameters of convex bodies
Imre Barany, Daniel Hug, Rolf Schneider
We prove sharp inequalities for the average number of affine diameters through the points of a convex body in . These inequalities hold if is either a polyto…