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Compression bounds for Lipschitz maps from the Heisenberg group to$L$_{1}

Jeff Cheeger Courant Institute, New York University Bruce Kleiner Courant Institute, New York University Assaf Naor Courant Institute, New York University

Analysis of PDEs Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1701.03006

Acta Mathematica, 207, (2), 291-373, 2009.11
We prove a quantitative bi-Lipschitz non-embedding theorem for the Heisenberg group with its Carnot–Carathéodory metric and apply it to give a lower bound on the integrality gap of the Goemans–Linial semidefinite relaxation of the sparsest cut problem.
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@inproceedings{jeff2009compression,
  title={Compression bounds for Lipschitz maps from the Heisenberg group to$L$_{1}},
  author={Jeff Cheeger, Bruce Kleiner, and Assaf Naor},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203357540742747},
  booktitle={Acta Mathematica},
  volume={207},
  number={2},
  pages={291-373},
  year={2009},
}
Jeff Cheeger, Bruce Kleiner, and Assaf Naor. Compression bounds for Lipschitz maps from the Heisenberg group to$L$_{1}. 2009. Vol. 207. In Acta Mathematica. pp.291-373. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203357540742747.
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