3 citations · 3 across the 9 of their papers we have counts for
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Exact Banach-Mazur distances of certain -sums and cones
Florian Grundbacher, Tomasz Kobos
We determine certain Banach-Mazur distances involving -direct sums of finite-dimensional real normed spaces and related cone constructions of convex bodies. Using a recent…
John-type decompositions for affinely-optimal positions of convex bodies
Florian Grundbacher, Tomasz Kobos
Many classical problems in convex geometry can be cast as optimization problems under certain containment conditions. The arguably best-understood example is volume-maximization of…
Equilateral dimension of the planar Banach--Mazur compactum
Tomasz Kobos, Konrad Swanepoel
We prove that there are arbitrarily large equilateral sets of planar and symmetric convex bodies in the Banach--Mazur distance. The order of the size of these -equilateral sets…
On Certain Extremal Banach-Mazur Distances and Ader's Characterization of Distance Ellipsoids
Florian Grundbacher, Tomasz Kobos
A classical consequence of the John Ellipsoid Theorem is the upper bound on the Banach-Mazur distance between the Euclidean ball and any symmetric convex body in $\mathb…
On the Banach-Mazur Distance in Small Dimensions
Tomasz Kobos, Marin Varivoda
We establish some results on the Banach-Mazur distance in small dimensions. Specifically, we determine the Banach-Mazur distance between the cube and its dual (the cross-polytope)…