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

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

2012-01-17

arxiv.org/abs/1201.3548v1

Mathematics

Metric Geometry

42 pages, 11 figures

Scientific paper

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 Poincar\'e inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincar\'e inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

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