5 papers · 1 filter
Tight Stability Estimates Near the Simplex and Applications for the Banach-Mazur Distance and Rogers-Shephard-Type Inequalities
René Brandenberg, Bernardo González Merino, Florian Grundbacher
We establish a tight stability estimate for the Minkowski asymmetry near its maximal value, improving earlier results in both the range for the admissible error and the strength of…
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…
Tightening Inequalities on Volume Extremal -Ellipsoids Using Asymmetry Measures
René Brandenberg, Florian Grundbacher
We consider two well-known problems: upper bounding the volume of lower dimensional ellipsoids contained in convex bodies given their John ellipsoid, and lower bounding the volume…
-Means of Convex Bodies: Sharpening Relations and Structural Properties
René Brandenberg, Florian Grundbacher
We study general -means of convex bodies, extending the classical definitions by W. J. Firey via support and gauge functions to two families ranging over all $p \in [-\infty,\in…