Let X be a space and let S ⊂ X with a measure of set size |S| and boundary size |∂S|. Fix a set C ⊂ X called the constraining set. The constrained isoperimetric problem asks when we can find a subset S of C that maximizes the Følner ratio FR(S) = |S|/|∂S|. We consider different measures for subsets of R^2,R^3,Z^2,Z^3 and describe the properties that must be satisfied for sets S that maximize the Folner ratio. We give explicit examples.
| Identifer | oai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-3699 |
| Date | 11 July 2011 |
| Creators | Do, Minh Nhat Vo |
| Publisher | BYU ScholarsArchive |
| Source Sets | Brigham Young University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
| Rights | http://lib.byu.edu/about/copyright/ |
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