A generalization of the Erdös-Szekeres convex n-gon theorem.
A geometric approach to correlation inequalities in the plane
By elementary geometric arguments, correlation inequalities for radially symmetric probability measures are proved in the plane. Precisely, it is shown that the correlation ratio for pairs of width-decreasing sets is minimized within the class of infinite strips. Since open convex sets which are symmetric with respect to the origin turn out to be width-decreasing sets, Pitt’s Gaussian correlation inequality (the two-dimensional case of the long-standing Gaussian correlation conjecture) is derived...
A Geometric Inequality and the Complexity of Computing Volume.
A geometric inequality involving a mobile point in the place of the triangle.
A geometric proof of some inequalities involving mixed volumes.
A Geometrical Characterization of Choquet Simplexes.
A Geometrical Isoperimetric Inequality and Applications to Problems of Mathematical Physics
A geometrical method in combinatorial complexity
A lower bound for the number of comparisons is obtained, required by a computational problem of classification of an arbitrarily chosen point of the Euclidean space with respect to a given finite family of polyhedral (non-convex, in general) sets, covering the space. This lower bound depends, roughly speaking, on the minimum number of convex parts, into which one can decompose these polyhedral sets. The lower bound is then applied to the knapsack problem.
A Helly number for unions of two boxes in .
A Helmholtz-Lie Type Characterization of Ellipsoids, I .
A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces
A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex...
A "hidden" characterization of polyhedral convex sets
We prove that a closed convex subset C of a complete linear metric space X is polyhedral in its closed linear hull if and only if no infinite subset A ⊂ X∖ C can be hidden behind C in the sense that [x,y]∩ C ≠ ∅ for any distinct x,y ∈ A.
A Linear-Time Algorithm for Computing the Voronoi Diagram of a Convex Polygon.
A linear-time construction of Reuleaux polygons.
À l'ombre de Loewner
A measure of asymmetry for domains of constant width.
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...
A measure of symmetry for ovals
A methodologically pure proof of a convex geometry problem.
A metric inequality associated with valuated fields