Modulus and Poincar\'e inequalities on non-self-similar Sierpinski carpets

Autor:	Mackay, John M., Tyson, Jeremy T., Wildrick, Kevin
Rok vydání:	2012
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry 30L99 31E05 28A80
Zdroj:	Geom. Funct. Anal. Volume 23, Number 3 (2013), 985-1034
Druh dokumentu:	Working Paper
DOI:	10.1007/s00039-013-0227-6
Popis:	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. Comment: v1: 42 pages, 11 figures. v2: 42 pages, 10 figures. Improved exposition
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1201.3548 Zobrazit plný text záznamu View this record from Arxiv