@article{d49ddba54f7940fc85043dec2d715022,
title = "Compression bounds for Lipschitz maps from the Heisenberg group to L 1 ",
abstract = "We prove a quantitative bi-Lipschitz non-embedding theorem for the Heisenberg group with its Carnot-Carath{\'e}odory metric and apply it to give a lower bound on the integrality gap of the Goemans-Linial semidefinite relaxation of the sparsest cut problem.",
author = "Jeff Cheeger and Bruce Kleiner and Assaf Naor",
note = "Funding Information: J.C. was supported in part by NSF grant DMS-0704404. B.K. was supported in part by NSF grant DMS-0805939. A.N. was supported in part by NSF grants CCF-0635078 and CCF-0832795, BSF grant 2006009 and the Packard Foundation.",
year = "2011",
month = dec,
doi = "10.1007/s11511-012-0071-9",
language = "English (US)",
volume = "207",
pages = "291--373",
journal = "Acta Mathematica",
issn = "0001-5962",
publisher = "Springer Netherlands",
number = "2",
}