Projections of the world onto convex polyhedra
Proof of a conjecture of Chan, Robbins, and Yuen.
Proof of Grünbaum's Conjecture on Common Transversals for Translates.
Properties of distance functions on convex surfaces and applications
If is a convex surface in a Euclidean space, then the squared intrinsic distance function is DC (d.c., delta-convex) on in the only natural extrinsic sense. An analogous result holds for the squared distance function from a closed set . Applications concerning -boundaries (distance spheres) and ambiguous loci (exoskeletons) of closed subsets of a convex surface are given.
Properties of typical bounded closed convex sets in Hilbert space.
Propriétés géométriques liées aux parenthésages d’un produit de facteurs. Application à une loi de composition partielle
Protecting regular polygons.
Pseudo-boundaries and pseudo-interiors for topological convexities [Book]
Pseudo-Petrie operators on Grünbaum polyhedra
Pseudo-self-affine tilings in .
Puzzles and polytope isomorphisms.
Qualitative and quantitative results for sets of singular points of convex bodies.
Quantitative Steinitz's Theorems with Applications to Multifingered Grasping.
Quasi Fricke Polygons and the Nielsen Convex Region.
Quasi polymatroidal flow networks.
Quasicrystallography: some interesting new patterns
Quasicrystals and almost periodic functions
We consider analogies between the "cut-and-project" method of constructing quasicrystals and the theory of almost periodic functions. In particular an analytic method of constructing almost periodic functions by means of convolution is presented. A geometric approach to critical points of such functions is also shown and illustrated with examples.
Quasisymmetric embedding of self similar surfaces and origami with rational maps.
Quaternionic geometry of matroids
Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper...
Quelques considérations concernant le problème de l'aguille de Buffon dans l'espace euclidien En.