Vertical versus horizontal Poincaré inequalities on the Heisenberg group

DOI10.1007/s11856-014-1088-xzbMath1312.46032arXiv1212.2107OpenAlexW2060280149MaRDI QIDQ476505

Vincent Lafforgue, Assaf Naor

Publication date: 2 December 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.2107

zbMATH Keywords

Banach spacePoisson semigroupsparsest cut problemdistortion of a bilipschitz mapGoemans-Linial algorithmmodulus of uniform convexity of power type \(q\)

Mathematics Subject Classification ID

Geometric group theory (20F65) Analysis on other specific Lie groups (43A80) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85) Geometric embeddings of metric spaces (30L05)

Related Items (14)

Vertical perimeter versus horizontal perimeter ⋮ Vertical versus horizontal Sobolev spaces ⋮ Estimates on the Markov convexity of Carnot groups and quantitative nonembeddability ⋮ Riesz transform and vertical oscillation in the Heisenberg group ⋮ Umbel convexity and the geometry of trees ⋮ A doubling subset of \(L_p\) for \(p>2\) that is inherently infinite dimensional ⋮ Dorronsoro's theorem in Heisenberg groups ⋮ Markov convexity and nonembeddability of the Heisenberg group ⋮ Coarse differentiation and quantitative nonembeddability for Carnot groups ⋮ Heat flow and quantitative differentiation ⋮ Impossibility of dimension reduction in the nuclear norm ⋮ No dimension reduction for doubling subsets of \(\ell_q\) when \(q>2\) revisited ⋮ Nonpositive curvature is not coarsely universal ⋮ Isomorphisms between spaces of Lipschitz functions

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