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

Mackay, John M.; Tyson, Jeremy T.; Wildrick, Kevin Michael (2013). Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets. Geometric and functional analysis, 23(3), pp. 985-1034. Birkhäuser 10.1007/s00039-013-0227-6

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Tyson, Jeremy and Wildrick, Kevin Michael

Subjects:

500 Science > 510 Mathematics

ISSN:

1016-443X

Publisher:

Birkhäuser

Language:

English

Submitter:

Mario Amrein

Date Deposited:

05 Jun 2014 14:52

Last Modified:

06 Mar 2019 14:58

Publisher DOI:

10.1007/s00039-013-0227-6

BORIS DOI:

10.7892/boris.41984

URI:

https://boris.unibe.ch/id/eprint/41984

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