Logarithmic bounds for isoperimetry and slices of convex sets

2023/03/27 by Bo’az Klartag, Klartag, Bo'az · 10 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2303.14938

openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Bourgain slicing conjecture and the Kannan-Lovász-Simonovits (KLS) isoperimetric conjecture in ℝⁿ hold true up to a factor of √(log n). A new ingredient used in the proof is an improved log-concave Lichnerowicz inequality.

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