6 papers · 1 filter
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-…
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…
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 we define to be the smallest possible factor to cover by a rescalation of and give…
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 : the intersection, the harmonic and the arithmetic mean, and the convex hull of and . A well-known result of…
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 the Harmonic mean of and can be optimally contained in the arithmetic mean of the same sets if and on…