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.
Citation
Jeff Cheeger. Bruce Kleiner. Assaf Naor. "Compression bounds for Lipschitz maps from the Heisenberg group to L1." Acta Math. 207 (2) 291 - 373, 2011. https://doi.org/10.1007/s11511-012-0071-9
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