A Cone of Inhomogeneous Second-Order Polynomials.
A local metric characterization of Banach spaces
A non-uniqueness theorem in the theory of Voronoi sets.
A taxicab version of the Erdős-Mordell theorem
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().
An O(n log n) Algorithm for the All-Nearest-Neighbors Problem.
Approximating Euclidean Distances by Small Degree Graphs*
Barbilian's metrization procedure in the plane yields either Riemannian or Lagrange generalized metrics
In the present paper we answer two questions raised by Barbilian in 1960. First, we study how far can the hypothesis of Barbilian's metrization procedure can be relaxed. Then, we prove that Barbilian's metrization procedure in the plane generates either Riemannian metrics or Lagrance generalized metrics not reducible to Finslerian or Langrangian metrics.
Block distance matrices.
Calcul du rayon de la sphère inscrite dans le tétraèdre
Classification of six-point metrics.
Diameter-Extremal Subsets of Spheres.
Distance-preserving maps in generalized polygons. I: Maps on flags.
Dividing an arc to subarcs with equal chords
Einbettung endlicher metrischer Räume
Euclidean and circum-Euclidean distance matrices: characterizations and linear preservers.
Geometry without topology as a new conception of geometry.
Homogeneity properties of hypercubes.
Hyperconvexity of ℝ-trees
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
Isometries on linear -normed spaces.