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 ΞΆ 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.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/70436 |
| Date | January 2011 |
| Contributors | Hardt, Robert M. |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 93 p., application/pdf |
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