A 2-manifold with boundary is a finite simple graph for which every unit sphere is a circular graph with 4 or more nodes or a path graph with 3 more nodes. The boundary is the set of vertices for which the unit sphere is a path graph, the interior is …
This is a presentation from Saturday, July 13, 2024. Curvatures are usually located on the zero dimensional part of space. I look here at curvature located on one or two dimensional parts of space. In the special case of a triangulation of a 2-dimensional surface, where the usual curvature is …
Here are three catchy open problems in differential geometry. As with any problem, we can look how to formulate discrete versions. The first problem is whether a positive curvature 2d manifold has positive Euler characteristic, the second is whether there is a positive curvature metric on and the third is …
The Curvature of graphs multplies under the Shannon product (strong product).
The Mickey mouse theorem assures that a connected positive curvature graph of positive dimension is a sphere.
The f-function of a graph minus 1 is the sum of the antiderivatives of the f-function anti-derivatives evaluated on the unit spheres.
