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Jeff Cheeger, Bruce Kleiner, Andrea Schioppa (2016)
Analysis and Geometry in Metric Spaces
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.
Jeff Cheeger, Bruce Kleiner (2015)
Analysis and Geometry in Metric Spaces
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,...
David M. Freeman (2014)
Analysis and Geometry in Metric Spaces
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.
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