A general notion of extreme subset
Relative extreme subsets
Carathéodory's and Helly's dimensions of products of convexity structures
О независимости точек метрического пространства
Convex half-spaces
Errata to the paper "Families of convex sets closed under intersection, homotheties and uniting increasing sequences of sets" Fundamenta Mathematicae 120 (1984), pp. 14-40
Families of convex sets closed under intersections, homotheties and uniting increasing sequences of sets
Superior estimation of Carathéodory's dimension for n-cell convexity
Terminal subsets of convex sets in finite-dimensional real normed spaces
Reduced spherical polygons
For every hemisphere K supporting a spherically convex body C of the d-dimensional sphere we consider the width of C determined by K. By the thickness Δ(C) of C we mean the minimum of the widths of C over all supporting hemispheres K of C. A spherically convex body is said to be reduced provided Δ(Z) < Δ(R) for every spherically convex body Z ⊂ R different from R. We characterize reduced spherical polygons on S². We show that every reduced spherical polygon is of thickness at most π/2. We...
Algebraic and geometric approach to the classification of semispaces.
Estimates for the Minimal Width of Polytopes Inscribed in Convex Bodies.
A measure of axial symmetry of centrally symmetric convex bodies
Denote by Kₘ the mirror image of a planar convex body K in a straight line m. It is easy to show that K*ₘ = conv(K ∪ Kₘ) is the smallest by inclusion convex body whose axis of symmetry is m and which contains K. The ratio axs(K) of the area of K to the minimum area of K*ₘ over all straight lines m is a measure of axial symmetry of K. We prove that axs(K) > 1/2√2 for every centrally symmetric convex body and that this estimate cannot be improved in general. We also give a formula for axs(P) for...
On-line algorithms for the -adic covering of the unit interval and for covering a cube by cubes.
Affine-regular hexagons of extreme areas inscribed in a centrally symmetric convex body.
On-line covering a box by cubes.
On-line packing sequences of segments, cubes and boxes.
Covering a three-dimensional convex body by smaller homothetic copies.
Characterizations of reduced polytopes in finite-dimensional normed spaces.
Banach-Mazur distance of central sections of a centrally symmetric convex body.
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