Geometric and Functional Analysis

, Volume 23, Issue 3, pp 985–1034 | Cite as

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

  • John M. Mackay
  • Jeremy T. Tyson
  • Kevin Wildrick
Article

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.

Keywords and phrases

Sierpiński carpet Doubling measure Modulus Poincaré inequality Gromov–Hausdorff tangent cone 

Mathematics Subject Classification (1991)

30L99 31E05 28A80 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • John M. Mackay
    • 1
  • Jeremy T. Tyson
    • 2
  • Kevin Wildrick
    • 3
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA
  3. 3.Mathematisches Institut, Universität BernBernSwitzerland

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