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arXiv · 1201.3548

Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets

John M. Mackay·Jeremy T. Tyson·Kevin Wildrick
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Abstract

A carpet is a metric space homeomorphic to the Sierpinski 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.

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John M. Mackay, Jeremy T. Tyson, Kevin Wildrick. 2013-02-01. Modulus and Poincaré inequalities on non-self-similar Sierpinski carpets. https://doi.org/10.1007/s00039-013-0227-6

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