An Equipartition of Planar Sets.
An exact method for the 2D guillotine strip packing problem.
An Example Concerning the Translative Kissing Number of a Convex Body.
An example of a flexible polyhedron with nonconstant volume in the spherical space.
An extension of Blaschke's theorem in the plane.
An extension of Fan's fixed point theorem and equilibrium point of an abstract economy
An Extension of Milman's Reverse Brunn-Minkowski Inequality.
An extension of the isoperimetric inequality on the sphere.
An illustrated theory of hyperbolic virtual polytopes
The paper gives an illustrated introduction to the theory of hyperbolic virtual polytopes and related counterexamples to A.D. Alexandrov’s conjecture.
An incomplete Voronoi tessellation
This paper presents distributional properties of a random cell structure which results from a growth process. It starts at the points of a Poisson point process. The growth is spherical with identical speed for all points; it stops whenever the boundaries of different cells have contact. The whole process finally stops after time t. So the space is not completely filled with cells, and the cells have both planar and spherical boundaries. Expressions are given for contact distribution functions,...
An inequality concerning edges of minor weight in convex 3-polytopes
Let be the number of edges in a convex 3-polytope joining the vertices of degree i with the vertices of degree j. We prove that for every convex 3-polytope there is ; moreover, each coefficient is the best possible. This result brings a final answer to the conjecture raised by B. Grünbaum in 1973.
An inequality for convex curves in the plane.
An Inequality for the Volume of Inscribed Ellipsoids.
An Infinite Family of Minor-Minimal Nonrealizable 3-Chirotopes.
An integral formula related to inner isoptics
An integral geometric theorem for simple valuations.
An Interactive Creation of Polyhedra Stellations with Various Symmetries
An intrinsic characterization of foldings of euclidean space
An Invariant Property of Balls in Arrangements of Hyperplanes.
An isomorphic Dvoretzky's theorem for convex bodies
We prove that there exist constants C>0 and 0 < λ < 1 so that for all convex bodies K in with non-empty interior and all integers k so that 1 ≤ k ≤ λn/ln(n+1), there exists a k-dimensional affine subspace Y of satisfying . This formulation of Dvoretzky’s theorem for large dimensional sections is a generalization with a new proof of the result due to Milman and Schechtman for centrally symmetric convex bodies. A sharper estimate holds for the n-dimensional simplex.