Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)985-1034
Number of pages50
JournalGeometric and Functional Analysis
Issue number3
StatePublished - Jun 2013


  • Doubling measure
  • Gromov-Hausdorff tangent cone
  • Modulus
  • Poincaré inequality
  • Sierpiński carpet

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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