Hardt, Robert M.2013-03-082013-03-082011Scott, Ryan Christopher. "Minimizing the mass of the codimension-two skeleton of a convex, volume-one polyhedral region." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/70436">https://hdl.handle.net/1911/70436</a>.https://hdl.handle.net/1911/70436In 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.93 p.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Pure sciencesPolyhedraConvex polytopesBounded variationMathematicsThesisScottRTHESIS MATH. 2011 SCOTT