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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…
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…
A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space
René Brandenberg, Bernardo González Merino, Mia Runge
We present a complete system of inequalities for the inradius, circumradius, and diameter in the -dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius…
Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
René Brandenberg, Mia Runge
We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number…