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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…