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Inverse Limit Spaces Satisfying a Poincaré Inequality

100%

Cheeger J., Kleiner B.

Analysis and Geometry in Metric Spaces

2015

tom 3

nr 1

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].

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

81%

Cheeger J., Kleiner B., Schioppa A.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

We prove metric differentiation for differentiability spaces in the sense of Cheeger [10, 14, 27]. As corollarieswe give a new proof of one of the main results of [14], a proof that the Lip-lip constant of any Lip-lip space in the sense of Keith [27] is equal to 1, and new nonembeddability results.

Ograniczanie wyników

2 Analysis and Geometry in Metric Spaces

2 Cheeger J.

2 Kleiner B.

1 Schioppa A.

1 2016

1 2015

Wyniki wyszukiwania

Inverse Limit Spaces Satisfying a Poincaré Inequality

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation