An Algorithm for Reconstructing Convex Bodies from Their Projections.
An alternative proof of Petty's theorem on equilateral sets
The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth point,...
An analogue of the Krein-Milman theorem for star-shaped sets.
An analytic solution to the Busemann-Petty problem on sections of convex bodies.
An application of the Hahn-Banach theorem in convex analysis
An arrangement of pseudocircles not realizable with circles.
An axiomatic approach for the Hajós theorem.
An edge-minimization problem for regular polygons.
An Ehrhart series formula for reflexive polytopes.
An Elementary Approach to Lower Bounds in Geometric Discrepancy.
An elementary chromatic reduction for gain graphs and special hyperplane arrangements.
An elementary proof of Blundon's inequality.
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.