Objects that Cannot Be Taken Apart with Two Hands.
On a Carathéodory's conjecture on umbilics : representing ovaloids
On a Conjectured Characterization of the Sphere.
On affine subspaces that illuminate a convex set.
On faces of a convex polyhedron in with a small number of sides.
On hyperbolic virtual polytopes and hyperbolic fans
Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ3 be a smooth convex body. If for a constant C, at every point of ∂K, we have R 1 ≤ C ≤ R 2 then K is a ball. (R 1 and R 2 stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular, a hyperbolic...
On optimal route planning evading cubes in the three space.
On the affine convexity of convex curves and hypersurfaces.
On the Connected Components of the Space of Line Transversals to a Family of Convex Sets.
On the Union of Jordan Regions and Collision-Free Translational Motion Amidst Polygonal Obstacles.
Parallelepipeds circumscribed about a convex body in 3-space.
Qualitative and quantitative results for sets of singular points of convex bodies.
Real analytic convex surfaces with positive topological entropy and rigid body dynamics.
Remark on a conjectured characterization of the sphere
Sets invariant under projections onto two dimensional subspaces
The Blaschke–Kakutani result characterizes inner product spaces , among normed spaces of dimension at least 3, by the property that for every 2 dimensional subspace there is a norm 1 linear projection onto . In this paper, we determine which closed neighborhoods of zero in a real locally convex space of dimension at least 3 have the property that for every 2 dimensional subspace there is a continuous linear projection onto with .
Singular sets of convex bodies and surfaces with generalized curvatures.
Testing of convex polyhedron visibility by means of graphs
This paper follows the article by V. Medek which solves the problem of finding the boundary of a convex polyhedron in both parallel and central projections. The aim is to give a method which yields a simple algorithm for the automation of an arbitrary graphic projection of a convex polyhedron. Section 1 of this paper recalls some necessary concepts from the graph theory. In Section 2 graphs are applied to determine visibility of a convex polyhedron.
The Complexity of Cutting Complexes.
The mean surface area of the boxes circumscribed about a convex body
Triangulation automatique d’un polyèdre en dimension