Addition and subtraction of homothety classes of convex sets.
Affine-regular hexagons of extreme areas inscribed in a centrally symmetric convex body.
Alexandrov’s theorem, weighted Delaunay triangulations, and mixed volumes
We present a constructive proof of Alexandrov’s theorem on the existence of a convex polytope with a given metric on the boundary. The polytope is obtained by deforming certain generalized convex polytopes with the given boundary. We study the space of generalized convex polytopes and discover a connection with weighted Delaunay triangulations of polyhedral surfaces. The existence of the deformation follows from the non-degeneracy of the Hessian of the total scalar curvature of generalized convex...
Algebraic and geometric approach to the classification of semispaces.
Algorithmen zur Unimodalitötsbestimmung einfacher Polygone
Almost sure asymptotic behaviour of the -neighbourhood surface area of Brownian paths
We show that whenever the -dimensional Minkowski content of a subset exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in , .
Ambiguous loci of the farthest distance mapping from compact convex sets
Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by the set of all X ∈ K() such that the farthest distance mapping is multivalued on a dense subset of . It is proved that is a residual dense subset of K().
Ambiguous Loci of the Metric Projection Onto Compact Starshaped Sets in a Banach Space.
An Algorithm for a Simple Construction of Suboptimal Digital Convex Polygons
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 Elementary Approach to Lower Bounds in Geometric Discrepancy.
An elementary proof of Blundon's inequality.
An Equipartition of Planar Sets.
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.