From the 1 of 5 linked papers with an AI index.
5 papers
Tight Stability Estimates Near the Simplex and Improved Bounds for the Diameter of the Banach-Mazur Compactum in Fixed Dimensions
René Brandenberg, Bernardo González Merino, Florian Grundbacher
The paper proves a sharp stability bound for the Minkowski asymmetry of convex bodies near its maximum, yielding precise estimates for their Banach‑Mazur distance to the simplex an…
-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…
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 lin…
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…