Vertical perimeter versus horizontal perimeter
From MaRDI portal
Publication:1643390
DOI10.4007/annals.2018.188.1.4zbMath1397.46020arXiv1701.00620OpenAlexW2963766025WikidataQ105337446 ScholiaQ105337446MaRDI QIDQ1643390
Publication date: 19 June 2018
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1701.00620
semidefinite programmingHeisenberg groupisoperimetric inequalityapproximation algorithmmetric embeddingsparsest cut problemmetric of negative type
Geometric group theory (20F65) Approximation algorithms (68W25) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85) Geometric embeddings of metric spaces (30L05)
Related Items
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups ⋮ Vertical versus horizontal Sobolev spaces ⋮ Harmonic intrinsic graphs in the Heisenberg group ⋮ Horizontally affine functions on step-2 Carnot algebras ⋮ Monotone sets and local minimizers for the perimeter in Carnot groups ⋮ Estimates on the Markov convexity of Carnot groups and quantitative nonembeddability ⋮ On the inner cone property for convex sets in two-step Carnot groups, with applications to monotone sets ⋮ Riesz transform and vertical oscillation in the Heisenberg group ⋮ Necessary condition for the L2 boundedness of the Riesz transform on Heisenberg groups ⋮ Composing and decomposing surfaces and functions ⋮ Precisely monotone sets in step-2 rank-3 Carnot algebras ⋮ Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group ⋮ Dorronsoro's theorem in Heisenberg groups ⋮ Singular integrals on regular curves in the Heisenberg group ⋮ Impossibility of dimension reduction in the nuclear norm ⋮ No dimension reduction for doubling subsets of \(\ell_q\) when \(q>2\) revisited ⋮ Plenty of big projections imply big pieces of Lipschitz graphs ⋮ The Andoni–Krauthgamer–Razenshteyn Characterization of Sketchable Norms Fails for Sketchable Metrics ⋮ Nonpositive curvature is not coarsely universal ⋮ Isomorphisms between spaces of Lipschitz functions ⋮ Polynomial and horizontally polynomial functions on Lie groups ⋮ Lipschitz graphs and currents in Heisenberg groups ⋮ Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
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