32 citations · 114 across the 14 of their papers we have counts for
8 papers · 1 filter
Thin Loewner carpets and their quasisymmetric embeddings in
Jeff Cheeger, Sylvester Eriksson-Bique
A carpet is a metric space which is homeomorphic to the standard Sierpiński carpet in , or equivalently, in . A carpet is called thin if its Hausdorff dimension…
Infinitesimal structure of differentiability spaces, and metric differentiation
Jeff Cheeger, Bruce Kleiner, Andrea Schioppa
We prove metric differentiation for differentiability spaces in the sense of Cheeger. As corollaries we give a new proof that the minimal generalized upper gradient coincides with…
Inverse limit spaces satisfying a Poincare inequality
Jeff Cheeger, Bruce Kleiner
We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs (and certain higher dimensional inverse systems of metric measure spaces) which imply tha…
Realization of metric spaces as inverse limits, and bilipschitz embedding in L_1
Jeff Cheeger, Bruce Kleiner
We give sufficient conditions for a metric space to bilipschitz embed in L_1. In particular, if X is a length space and there is a Lipschitz map u:X--->R such that for every interv…
Compression bounds for Lipschitz maps from the Heisenberg group to
Jeff Cheeger, Bruce Kleiner, Assaf Naor
We prove a quantitative bi-Lipschitz nonembedding theorem for the Heisenberg group with its Carnot-Carathéodory metric and apply it to give a lower bound on the integrality gap of…
Metric differentiation, monotonicity and maps to L^1
Jeff Cheeger, Bruce Kleiner
We give a new approach to the infinitesimal structure of Lipschitz maps into L^1. As a first application, we give an alternative proof of the main theorem from an earlier paper, th…