Compression bounds for Lipschitz maps from the Heisenberg group to L 1

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)291-373
Number of pages83
JournalActa Mathematica
Volume207
Issue number2
DOIs
StatePublished - Dec 2011

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Lipschitz Map
Semidefinite Relaxation
Integrality
Heisenberg Group
Lipschitz
Compression
Lower bound
Metric
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Compression bounds for Lipschitz maps from the Heisenberg group to L 1 . / Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf.

In: Acta Mathematica, Vol. 207, No. 2, 12.2011, p. 291-373.

Research output: Contribution to journalArticle

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