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.
Curves and lattices of points in the Minkowski plane
Curves in P² and symplectic packings.
Cutting Disjoint Disks by Straight Lines.
Cutting Hyperplane Arrangements.
Cutting Hyperplanes for Divide-and-Conquer.
Cylinder and horoball packing in hyperbolic space.