From the 1 of 4 linked papers with an AI index.
4 papers
On the Log-submodularity for zonoids: from Mixed Volume inequalities to the Hypercube
Gennadiy Averkov, Katherina von Dichter, Ivan Soprunov
We prove a log-submodularity-type inequality for zonoids in , extending the three-dimensional result of Fradelizi, Madiman, Meyer, and Zvavitch. More generally, we co…
Mixed volumes of zonoids and the absolute value of the Grassmannian
Gennadiy Averkov, Katherina von Dichter, Simon Richard +1
The paper develops a combinatorial framework linking mixed volumes of zonoids with the absolute value image of the Grassmannian, and uses polyhedral computations to produce new Min…
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…
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 with respect to reflections across affine subspaces of a given dimension. We pro…