On the structure of the quadratic Boolean problem polytope
On the Sum of a Zonotope and an Ellipsoid
On the symmetric difference metric for convex bodies.
On the thinnest 2-fold double-lattice covering with a centrally symmetric convex domain. (Über die dünnste doppelgitterförmige 2-fache Überdeckung mit einem zentralsymmetrischen konvexen Bereich.)
On the Union of Jordan Regions and Collision-Free Translational Motion Amidst Polygonal Obstacles.
On the volume method in the study of Auerbach bases of finite-dimensional normed spaces
In this note we show that if the ratio of the minimal volume V of n-dimensional parallelepipeds containing the unit ball of an n-dimensional real normed space X to the maximal volume v of n-dimensional crosspolytopes inscribed in this ball is equal to n!, then the relation of orthogonality in X is symmetric. Hence we deduce the following properties: (i) if V/v=n! and if n>2, then X is an inner product space; (ii) in every finite-dimensional normed space there exist at least two different Auerbach...
On the volume of a certain polytope.
On the Volume of Equichordal Sets.
On the volume of the double stochastic matrices.
On the volume of the polytope of doubly stochastic matrices.
On the volume of unbounded polyhedra in the hyperbolic space.
On the volumes of hyperbolic 5-orthoschemes and the Trilogarithm.
On the Weight of Minor Faces in Triangle-Free 3-Polytopes
The weight w(f) of a face f in a 3-polytope is the degree-sum of vertices incident with f. It follows from Lebesgue’s results of 1940 that every triangle-free 3-polytope without 4-faces incident with at least three 3-vertices has a 4-face with w ≤ 21 or a 5-face with w ≤ 17. Here, the bound 17 is sharp, but it was still unknown whether 21 is sharp. The purpose of this paper is to improve this 21 to 20, which is best possible.
On the Zone of a Surface in a Hyperplane Arrangement.
On the ψ₂-behaviour of linear functionals on isotropic convex bodies
The slicing problem can be reduced to the study of isotropic convex bodies K with , where is the isotropic constant. We study the ψ₂-behaviour of linear functionals on this class of bodies. It is proved that for all θ in a subset U of with measure σ(U) ≥ 1 - exp(-c√n). However, there exist isotropic convex bodies K with uniformly bounded geometric distance from the Euclidean ball, such that . In a different direction, we show that good average ψ₂-behaviour of linear functionals on an isotropic...
On tropical Kleene star matrices and alcoved polytopes
In this paper we give a short, elementary proof of a known result in tropical mathematics, by which the convexity of the column span of a zero-diagonal real matrix is characterized by being a Kleene star. We give applications to alcoved polytopes, using normal idempotent matrices (which form a subclass of Kleene stars). For a normal matrix we define a norm and show that this is the radius of a hyperplane section of its tropical span.
On Tucker's key theorem.
On two classes of Banach spaces with uniform normal structure
On Two Conjectures of Franz Hering About Convex Surfaces.
On Two Finite Covering Problems of Bambah, Rogers, Woods and Zassenhaus.