On a question of Milman and Alesker concerning the monotonicity of a domain functional.
On a special family of compact convex sets in the Euclidean plane .
On a Spherical Integral Transformation and Sections of Star Bodies.
On a statistical approach to Bertrand's problem.
On affine subspaces that illuminate a convex set.
On an Ordering for Probability Measures and a Corresponding Integral Representation.
On Antipodal and Adjoint Pairs of Points for Two Convex Bodies.
On area and side lengths of triangles in normed planes
Let be a d-dimensional normed space with norm ||·|| and let B be the unit ball in . Let us fix a Lebesgue measure in with . This measure will play the role of the volume in . We consider an arbitrary simplex T in with prescribed edge lengths. For the case d = 2, sharp upper and lower bounds of are determined. For d ≥ 3 it is noticed that the tight lower bound of is zero.
On areas and integral geometry in Minkowski spaces.
On Asymptotic Volume of Tori.
On Averaging Multisets.
On Bárány's theorems of Carathéodory and Helly type
The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads as follows:...
On Barbier's theorem
On billiard arcs
On boundaries of unions of sets with positive reach.
On boundary arcs joining antipodal points of a planar convex body.
On Buffon's problem for a lattice and its deformations.
On Busemann surface area of the unit ball in Minkowski spaces.
On Carathéodory's and Krein-Milman's theorems in fully ordered groups
On certain random polygons of large areas.