17 citations · 40 across the 17 of their papers we have counts for
19 papers
Jung-type Inequalities and Blaschke-Santaló Diagrams for Different Diameter Variants
René Brandenberg, Mia Runge
We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number…
Extremal solutions for Network Flow with Differential Constraints -- A Generalization of Spanning Trees
René Brandenberg, Paul Stursberg
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is t…
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…
On -Blaschke-Santaló diagrams with regular -gon gauges
René Brandenberg, Bernardo González Merino
We provide a study of Blaschke-Santaló diagrams for the inradius, diameter, and circumradius, measured with respect to different gauges. This contrasts previous works on those diag…
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…