Minimizing the mass of the codimension-two skeleton of a convex, volume-one polyhedral region
Scott, Ryan Christopher
Hardt, Robert M.
Doctor of Philosophy
In this paper we establish the existence and partial regularity of a (d-2)-dimensional edge-length minimizing polyhedron in [Special characters omitted.] . The minimizer is a generalized convex polytope of volume one which is the limit of a minimizing sequence of polytopes converging in the Hausdorff metric. We show that the (d-2)-dimensional edge-length ζ d -2 is lower-semicontinuous under this sequential convergence. Here the edge set of the limit generalized polytope is a closed subset of the boundary whose complement in the boundary consists of countably many relatively open planar regions.
Pure sciences; Polyhedra; Convex polytopes; Bounded variation; Mathematics