Inverse Limit Spaces Satisfying a Poincaré Inequality
Abstract: We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [12]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of examples for which our conditions are satisfied. Included are known examples of PI spaces, such as Laakso spaces, and a large class of new examples. As follows easily from [4], generically our examples have the property that they do not bilipschitz embed in any Banach space with Radon-Nikodym property. For Laakso spaces, thiswas noted in [4]. However according to [7] these spaces admit a bilipschitz embedding in L1. For Laakso spaces, this was announced in [5].
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Inverse Limit Spaces Satisfying a Poincaré Inequality ; volume:3 ; number:1 ; year:2015 ; extent:25
Analysis and geometry in metric spaces ; 3, Heft 1 (2015) (gesamt 25)
- Creator
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Cheeger, Jeff
Kleiner, Bruce
- DOI
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10.1515/agms-2015-0002
- URN
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urn:nbn:de:101:1-2024041116261999015289
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
- 14.08.2025, 10:56 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Cheeger, Jeff
- Kleiner, Bruce
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