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Relating Modulus and Poincaré Inequalities on Modified Sierpiński Carpets

Title:

Relating Modulus and Poincaré Inequalities on Modified Sierpiński Carpets

Fenwick, Andrew R. D. (2012) Relating Modulus and Poincaré Inequalities on Modified Sierpiński Carpets. Masters thesis, Concordia University.

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Abstract

This thesis investigates the question of whether a doubling metric measure space supports a Poincar\'e inequality and explains the relationship between the existence of such an inequality and the non-triviality of the respective modulus. It discusses in detail a general class of modified Sierpi\'nski carpets presented by Mackay, Tyson, and Wildrick~\cite{M & T & K}, which are the first examples of spaces that support Poincar\'e inequalities for a renormalized Lebesgue measure that are also compact subsets of Euclidean space with empty interior. It describes the intricate relationship between the sequence used in the construction of a modified Sierpi\'nski carpet and the validity of Poincar\'e inequalities on that space.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Fenwick, Andrew R. D.
Institution:Concordia University
Degree Name:M.A.
Program:Mathematics
Date:12 August 2012
Thesis Supervisor(s):Dafni, Galia
ID Code:974700
Deposited By:ANDREW FENWICK
Deposited On:30 Oct 2012 11:08
Last Modified:30 Oct 2012 11:08
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