Modulus and Poincar\'e inequalities on non-self-similar Sierpinski   carpets
  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. 
John M. Mackay, Jeremy T. Tyson and Kevin Wildrick
math.MG math.DG