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6 papers · 1 filter
Lipschitz extensions into Jet space Carnot groups
Stefan Wenger, Robert Young
The aim of this article is to prove a Lipschitz extension theorem for partially defined Lipschitz maps to jet spaces endowed with a left-invariant sub-Riemannian Carnot-Carathéodor…
Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property
Jeff Cheeger, Bruce Kleiner
We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincaré inequality, and V is a Banach spac…
Embeddings of discrete groups and the speed of random walks
Assaf Naor, Yuval Peres
For a finitely generated group G and a banach space X let α^*_X(G) (respectively α^#_X(G)) be the supremum over all α\ge 0 such that there exists a Lipschitz mapping (respectively…
The Euclidean distortion of the lamplighter group
Tim Austin, Assaf Naor, Alain Valette
We show that the cyclic lamplighter group $C_2 \bwr C_n$ embeds into Hilbert space with distortion . This matches the lower bound proved by Lee, Naor and Pe…
Characterizations of metric trees and Gromov hyperbolic spaces
Stefan Wenger
In a recent paper Chatterji and Niblo proved that a geodesic metric space is Gromov hyperbolic if and only if the intersection of any two closed balls has uniformly bounded eccentr…
Euclidean distortion and the Sparsest Cut
Sanjeev Arora, James R. Lee, Assaf Naor
We prove that every -point metric space of negative type (and, in particular, every -point subset of ) embeds into a Euclidean space with distortion $O(\sqrt{\log n} \cd…