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math.MG2026
On the Perelman-Pukhov quotient of successive radii: better and asymptotically optimal bounds
Bernardo González Merino, Beatriz Marín Gimeno, Mia Runge
Perel'man in 1987 and independently Pukhov in 1979 proved that the quotient between the -th successive outer radius and the -th successive inner radius of a convex body…
math.MG2026
Minimization of the inradius of convex bodies for prescribed diameter and circumradius in Minkowski spaces
René Brandenberg, Bernardo González Merino, Mia Runge
We study Blaschke-Santaló diagrams for the inradius, circumradius, and diameter in arbitrary-dimensional Minkowski spaces. Their boundary parts are regularly described by four line…