@article{52ed3d49e4fe4cd2810cf7452945b708,
title = "Modulus and Poincar{\'e} Inequalities on Non-Self-Similar Sierpi{\'n}ski Carpets",
abstract = "A carpet is a metric space homeomorphic to the Sierpi{\'n}ski 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.",
keywords = "Doubling measure, Gromov-Hausdorff tangent cone, Modulus, Poincar{\'e} inequality, Sierpi{\'n}ski carpet",
author = "Mackay, {John M.} and Tyson, {Jeremy T.} and Kevin Wildrick",
note = "Funding Information: Keywords and phrases: Sierpi{\'n}ski carpet, Doubling measure, Modulus, Poincar{\'e} inequality, Gromov–Hausdorff tangent cone Mathematics Subject Classification (1991): 30L99; 31E05; 28A80 J. M. Mackay and J. T. Tyson were supported by US National Science Foundation Grant DMS-0901620. J. M. Mackay was supported by EPSRC grant “Geometric and analytic aspects of infinite groups”. J. T. Tyson was supported by US National Science Foundation Grant DMS-1201875. K. Wildrick supported by Academy of Finland Grants 120972 and 128144, the Swiss National Science Foundation, ERC Project CG-DICE, and European Science Council Project HCAA.",
year = "2013",
month = jun,
doi = "10.1007/s00039-013-0227-6",
language = "English (US)",
volume = "23",
pages = "985--1034",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkhauser Verlag Basel",
number = "3",
}