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MODULUS AND POINCARÉ INEQUALITIES ON NON-SELF-SIMILAR SIERPIŃSKI CARPETS

By John M. Mackay, Jeremy T. Tyson and Kevin Wildrick

Abstract

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

Publisher: 2013-09-27
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.3194
Provided by: CiteSeerX
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