3 citations · 3 across the 9 of their papers we have counts for
10 papers
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…
A Complex Analogue of Spencer's Six Standard Deviations Theorem and the Complex Banach-Mazur Distance
Tomasz Kobos, Marin Varivoda
We investigate a complex analogue of Spencer's Six Standard Deviations Theorem. Specifically, we propose the following conjecture: for any dimension , given vectors $a_1,…
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)…
On non-linear mappings preserving the semi-inner product
Tomasz Kobos, Paweł Wójcik
We say that a smooth normed space has a property (SL), if every mapping preserving the semi-inner product on is linear. It is well known that every Hilbert spac…
A uniform lower bound on the norms of hyperplane projections of spherical polytopes
Tomasz Kobos
Let be a centrally symmetric spherical and simplicial polytope, whose vertices form a net in the unit sphere in . We prove a uniform lower bound on…
Extremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane
Tomasz Kobos
We prove that if are convex bodies such that is symmetric and the Banach-Mazur distance between and is equal to , then is a triangle.
Stability result for the extremal Grünbaum distance between convex bodies
Tomasz Kobos
In 1963 Grünbaum introduced the following variation of the Banach-Mazur distance for arbitrary convex bodies : $d_G(K, L) = \inf \{ |r| \ : \ K' \subset…