Covering abelian groups with cyclic subsets.
Covering belt bodies by smaller homothetical copies.
Covering large balls with convex sets in spherical space.
Covering space with convex bodies
Covering the plane with congruent copies of a convex disk.
Covering the Plane with Convex Polygons.
Covering the Plane with Two Kinds of Circles.
Covering the sphere with 11 equal circles.
Covering the unit cube by equal balls.
Covering the unit square by squares.
Coverings Sets for Plane Lattices.
Coxeter group actions on the complement of hyperplanes and special involutions
We consider both standard and twisted actions of a (real) Coxeter group on the complement to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in and give explicit formulae which describe both actions on the total cohomology in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group , the Weyl groups...
Crofton measures in polytopal Hilbert geometries.
Cube tilings as contributions of algebra to geometry.
Cube-Tilings of Rn and Nonlinear Codes.
Cubic partial cubes from simplicial arrangements.
Curvature and Flow in Digital Space
We first define the curvature indices of vertices of digital objects. Second, using these indices, we define the principal normal vectors of digital curves and surfaces. These definitions allow us to derive the Gauss-Bonnet theorem for digital objects. Third, we introduce curvature flow for isothetic polytopes defined in a digital space.
Curvature and -strict convexity.
Curvature flows of maximal integral triangulations
This paper describes local configurations of some planar triangulations. A Gauss-Bonnet-like formula holds locally for a kind of discrete “curvature” associated to such triangulations.
Curvature on a graph via its geometric spectrum
We approach the problem of defining curvature on a graph by attempting to attach a ‘best-fit polytope’ to each vertex, or more precisely what we refer to as a configured star. How this should be done depends upon the global structure of the graph which is reflected in its geometric spectrum. Mean curvature is the most natural curvature that arises in this context and corresponds to local liftings of the graph into a suitable Euclidean space. We discuss some examples.