Geodesic
Inverse Limit Spaces Satisfying a Poincaré Inequality
Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1 Cet article a éte moissonné depuis la source The Polish Digital Mathematics Library

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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].
Mots-clés : Convergent inverse systems, metric measure graphs, PI space 
@article{AGMS_2015_3_1_a2,
     author = {Cheeger, Jeff and Kleiner, Bruce},
     title = {Inverse {Limit} {Spaces} {Satisfying} a {Poincar\'e} {Inequality}},
     journal = {Analysis and Geometry in Metric Spaces},
     year = {2015},
     volume = {3},
     number = {1},
     zbl = {1331.46016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a2/}
}
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Cheeger, Jeff; Kleiner, Bruce. Inverse Limit Spaces Satisfying a Poincaré Inequality. Analysis and Geometry in Metric Spaces, Tome 3 (2015) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2015_3_1_a2/