Modulus and Poincar\'e inequalities on non-self-similar Sierpinski carpets
Metric Geometry
2013-11-12 v2 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1201.3548,
title = {Modulus and Poincar\'e inequalities on non-self-similar Sierpinski carpets},
author = {John M. Mackay and Jeremy T. Tyson and Kevin Wildrick},
journal= {arXiv preprint arXiv:1201.3548},
year = {2013}
}
Comments
v1: 42 pages, 11 figures. v2: 42 pages, 10 figures. Improved exposition