A Geometric Realization Without Self-Intersections Does Exist for Dyck's Regular Map.
A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces
A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex...
A modification of Graham's algorithm for determining the convex hull of a finite planar set.
A new algebraic criterion for shellability.
A New Formula for the Volume of Lattice Polyhedra.
A New Index for Polytopes.
A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.
A non-uniqueness theorem in the theory of Voronoi sets.
A Note on Geometry of Polyhedron of Three-index Transportation Problem
A Note on Small Linear-Ordering Polytopes.
A note on the existence of -equivelar polyhedral maps.
A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra.
A point in many triangles.
A quantitative Steinitz' theorem.
A rough curvature-dimension condition for metric measure spaces
We introduce and study a rough (approximate) curvature-dimension condition for metric measure spaces, applicable especially in the framework of discrete spaces and graphs. This condition extends the one introduced by Karl-Theodor Sturm, in his 2006 article On the geometry of metric measure spaces II, to a larger class of (possibly non-geodesic) metric measure spaces. The rough curvature-dimension condition is stable under an appropriate notion of convergence, and stable under discretizations as...
A short introduction to shadows of 4-manifolds
We give a self-contained introduction to the theory of shadows as a tool to study smooth 3-manifolds and 4-manifolds. The goal of the present paper is twofold: on the one hand, it is intended to be a shortcut to a basic use of the theory of shadows, on the other hand it gives a sketchy overview of some of the most recent results on shadows. No original result is proved here and most of the details of the proofs are left out.
A short proof of rigidity of convex polytopes.
A simpler construction of volume polynomials for a polyhedron.
A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria
Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending...
A theorem on nonexistence of a certain type of nearly regular cell-decompositions of the sphere