Abstract
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.
Degree
MS
College and Department
Physical and Mathematical Sciences; Mathematics
Rights
http://lib.byu.edu/about/copyright/
BYU ScholarsArchive Citation
Do, Minh Nhat Vo, "The Constrained Isoperimetric Problem" (2011). Theses and Dissertations. 2700.
https://scholarsarchive.byu.edu/etd/2700
Date Submitted
2011-07-11
Document Type
Thesis
Handle
http://hdl.lib.byu.edu/1877/etd4636
Keywords
amenability, isoperimetric, Folner ratio, cooling function, cooling field
Language
English