On the radius of a set in a Hilbert space
On the section of a lattice–covering of balls
On the symmetric difference metric for convex bodies.
On the Union of Jordan Regions and Collision-Free Translational Motion Amidst Polygonal Obstacles.
On the volume of a certain polytope.
On the Volume of Equichordal Sets.
On the volume of the double stochastic matrices.
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 Two Finite Covering Problems of Bambah, Rogers, Woods and Zassenhaus.
On unit balls and isoperimetrices in normed spaces
The purpose of this paper is to continue the investigations on the homothety of unit balls and isoperimetrices in higher-dimensional Minkowski spaces for the Holmes-Thompson measure and the Busemann measure. Moreover, we show a strong relation between affine isoperimetric inequalities and Minkowski geometry by proving some new related inequalities.
On Weak Tail Domination of Random Vectors
Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
One functional-analytical idea by Alexandrov in convex geometry.
Optimierung konstant belegter Ovale und ein Hyperbel-Schnittsatz
Optimizing geometric measures for fixed minimal annulus and inradius.