On properties of geodesic -preinvex functions.
On reduced pairs of bounded closed convex sets.
In this paper certain criteria for reduced pairs of bounded closed convex set are presented. Some examples of reduced and not reduced pairs are enclosed.
On Reuleaux triangles in Minkowski planes.
On rhombic dodecahedra.
On Schläfli's reduction formula.
On Separating Two Simple Polygons by a Single Translation.
On set covariance and three-point test sets
The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic...
On seven points in the boundary of a plane convex body in large relative distances.
On shadow boundaries of centrally symmetric convex bodies.
On smooth points of boundaries of open sets
The notions of smooth points of the boundary of an open set and α(·) intrinsically paraconvex sets are introduced. It is shown that for an α(·) intrinsically paraconvex open set the set of smooth points is a dense -set of the boundary.
On some classes of curves in a projective space
On some packings of the hyperbolic plane by incongruent hypercyclic domains.
On some properties of hyperconvex spaces.
On some random convex sets
On some special surfaces connected with convex surfaces of the Lobachevskij space.
On some vector balancing problems
Let V be an origin-symmetric convex body in , n≥ 2, of Gaussian measure . It is proved that for every choice of vectors in the Euclidean unit ball , there exist signs with . The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin.
On splitting infinite-fold covers
Let X be a set, κ be a cardinal number and let ℋ be a family of subsets of X which covers each x ∈ X at least κ-fold. What assumptions can ensure that ℋ can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover ℋ: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly ordered sets and covers of ℝⁿ by polyhedra and by arbitrary convex sets. We focus on...
On star duality of mixed intersection bodies.
On starshapedness of the union of closed sets in
On support functions of Compact Convex Sets.