Katherina von Dichter

activity

20202026

collaborators

7 papers

math.MG2026

On the Log-submodularity for zonoids: from Mixed Volume inequalities to the Hypercube

Gennadiy Averkov, Katherina von Dichter, Ivan Soprunov

In convex geometry, a number of inequalities for the volume of coordinate projections of convex bodies share a common structural property. We formalize them as inequalities of log-…

math.MG2025

Bounding the diameter-width ratio using containment inequalities of means of convex bodies

Katherina von Dichter, Mia Runge

We completely describe the region of possible values of the diameter-width ratio for planar pseudo-complete sets in dependence of the Minkowski asymmetry. In order to do this, we f…

math.MG2025

Minkowski chirality: a measure of reflectional asymmetry of convex bodies

Andrei Caragea, Katherina von Dichter, Kurt Klement Gottwald +3

Using an optimal containment approach, we quantify the asymmetry of convex bodies in $R^{n}$ with respect to reflections across affine subspaces of a given dimension. We pro…

math.CO2024

Mixed volumes of zonoids and the absolute value of the Grassmannian

Gennadiy Averkov, Katherina von Dichter, Simon Richard +1

Zonoids are Hausdorff limits of zonotopes, while zonotopes are convex polytopes defined as the Minkowski sums of finitely many segments. We present a combinatorial framework that l…

math.MG2023

From inequalities relating symmetrizations of convex bodies to the diameter-width ratio for complete and pseudo-complete convex sets

René Brandenberg, Katherina von Dichter, Bernardo González Merino

For a Minkowski centered convex compact set $K$ we define $α (K)$ to be the smallest possible factor to cover $K \cap (- K)$ by a rescalation of $conv (K \cup (- K))$ and give…

math.MG2021

Tightening and reversing the arithmetic-harmonic mean inequality for symmetrizations of convex sets

René Brandenberg, Katherina von Dichter, Bernardo González Merino

This paper deals with four symmetrizations of a convex set $C$ : the intersection, the harmonic and the arithmetic mean, and the convex hull of $C$ and $- C$ . A well-known result of…

math.MG2020

Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio

René Brandenberg, Katherina von Dichter, Bernardo González Merino

We show that for any Minkowski centered planar convex compact set $C$ the Harmonic mean of $C$ and $- C$ can be optimally contained in the arithmetic mean of the same sets if and on…