# Inverse Limit Spaces Satisfying a Poincaré Inequality

Analysis and Geometry in Metric Spaces (2015)

- Volume: 3, Issue: 1, page 15-39, electronic only
- ISSN: 2299-3274

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topJeff Cheeger, and Bruce Kleiner. "Inverse Limit Spaces Satisfying a Poincaré Inequality." Analysis and Geometry in Metric Spaces 3.1 (2015): 15-39, electronic only. <http://eudml.org/doc/268843>.

@article{JeffCheeger2015,

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].},

author = {Jeff Cheeger, Bruce Kleiner},

journal = {Analysis and Geometry in Metric Spaces},

keywords = {Convergent inverse systems; metric measure graphs; PI space; convergent inverse systems; Poincaré inequality; Radon-Nikodým property},

language = {eng},

number = {1},

pages = {15-39, electronic only},

title = {Inverse Limit Spaces Satisfying a Poincaré Inequality},

url = {http://eudml.org/doc/268843},

volume = {3},

year = {2015},

}

TY - JOUR

AU - Jeff Cheeger

AU - Bruce Kleiner

TI - Inverse Limit Spaces Satisfying a Poincaré Inequality

JO - Analysis and Geometry in Metric Spaces

PY - 2015

VL - 3

IS - 1

SP - 15

EP - 39, electronic only

AB - 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].

LA - eng

KW - Convergent inverse systems; metric measure graphs; PI space; convergent inverse systems; Poincaré inequality; Radon-Nikodým property

UR - http://eudml.org/doc/268843

ER -

## References

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