Bourgain's slicing problem and KLS isoperimetry up to polylog

DOI10.1007/s00039-022-00612-9OpenAlexW4285545993MaRDI QIDQ2088129

Joseph Lehec, Bo'az Klartag

Publication date: 21 October 2022

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.15551

zbMATH Keywords

slicing problemBourgain's hyperplane conjectureKLS isoperimetric conjecture

Mathematics Subject Classification ID

Probability measures on topological spaces (60B05) Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (13)

Self-improvement of the Bakry-Emery criterion for Poincaré inequalities and Wasserstein contraction using variable curvature bounds ⋮ A note on the reduction of the slicing problem to centrally symmetric convex bodies ⋮ On a multi-integral norm defined by weighted sums of log-concave random vectors ⋮ Comparison problems for Radon transforms ⋮ Long lines in subsets of large measure in high dimension ⋮ Tyler's and Maronna's M-estimators: non-asymptotic concentration results ⋮ Unnamed Item ⋮ A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures ⋮ The Langevin Monte Carlo algorithm in the non-smooth log-concave case ⋮ Half-space depth of log-concave probability measures ⋮ Stability of the isodiametric problem on the sphere and in the hyperbolic space ⋮ Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs ⋮ Threshold for the expected measure of random polytopes

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