Lp metrics on the Heisenberg group and the Goemans-Linial conjecture

We prove that the function d : R3 × R3 → [0, ∞) given by d (x, y, z), (t, u, v) = (t − x)2 + (u − y)2 2 + (v − z + 2xu − 2yt)2 1 2 + (t − x)2 + (u − y)2 1 2 . is a metric on R3 such that (R3 , √ d) is isometric to a subset of Hilbert space, yet (R3 , d) does

• Type: Conference
• Year: 2006
• Where: FOCS
• Authors: James R. Lee, Assaf Naor
• Keywords: FOCS 2006, Metric, Theoretical Computer Science