Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\)

DOI10.1007/s11511-012-0071-9zbMath1247.46020arXiv0910.2026OpenAlexW1995977886WikidataQ102217943 ScholiaQ102217943MaRDI QIDQ416849

Jeff Cheeger, Assaf Naor, Bruce Kleiner

Publication date: 10 May 2012

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.2026

zbMATH Keywords

Heisenberg groupbilipschitz embeddingCarnot-Carathéodory distanceGoemans-Linial conjecturesparsest cut problem

Mathematics Subject Classification ID

Geometric group theory (20F65) Analysis on real and complex Lie groups (22E30) Distance in graphs (05C12) Approximation algorithms (68W25) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85)

Related Items (30)

Sketching and Embedding are Equivalent for Norms ⋮ Metric Characterizations of Some Classes of Banach Spaces ⋮ Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group ⋮ Vertical perimeter versus horizontal perimeter ⋮ Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces ⋮ Discretization and affine approximation in high dimensions ⋮ Metric differentiation, monotonicity and maps to \(L^{1}\) ⋮ Horizontally affine functions on step-2 Carnot algebras ⋮ Monotone sets and local minimizers for the perimeter in Carnot groups ⋮ On the inner cone property for convex sets in two-step Carnot groups, with applications to monotone sets ⋮ Precisely monotone sets in step-2 rank-3 Carnot algebras ⋮ Lower bounds on Ricci curvature and quantitative behavior of singular sets ⋮ A doubling subset of \(L_p\) for \(p>2\) that is inherently infinite dimensional ⋮ Vertical versus horizontal Poincaré inequalities on the Heisenberg group ⋮ Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group ⋮ Markov convexity and nonembeddability of the Heisenberg group ⋮ Equivalent definitions of \(BV\) space and of total variation on metric measure spaces ⋮ Coarse differentiation and quantitative nonembeddability for Carnot groups ⋮ Bourgain's discretization theorem ⋮ Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents ⋮ Quantitative geometry ⋮ Heat flow and quantitative differentiation ⋮ Inverse limit spaces satisfying a Poincaré inequality ⋮ Differentiating maps into \(L^1\), and the geometry of BV functions ⋮ No dimension reduction for doubling subsets of \(\ell_q\) when \(q>2\) revisited ⋮ The Andoni–Krauthgamer–Razenshteyn Characterization of Sketchable Norms Fails for Sketchable Metrics ⋮ Quantitative affine approximation for UMD targets ⋮ Polynomial and horizontally polynomial functions on Lie groups ⋮ Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding ⋮ The Lip-lip equality is stable under blow-up

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