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Isoperimetric inequalities in high-dimensional convex sets

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arxiv 2406.01324 v2 pith:F4FSFG6S submitted 2024-06-03 math.FA math.PR

Bo'az Klartag , Joseph Lehec This is my paper · ORCID
classification math.FAmath.PR
keywords isoperimetricbourgainconjectureconvexfocusinghigh-dimensionalinequalitieskannan
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These are lecture notes focusing on recent progress towards Bourgain's slicing problem and the isoperimetric conjecture proposed by Kannan, Lovasz and Simonovits (KLS).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Distances between non-symmetric convex bodies: optimal bounds up to polylog

    math.MG 2025-10 conditional novelty 8.0 of 10

    The Banach–Mazur distance between arbitrary convex bodies in R^n is at most n·polylog(n), and with 99% volume containment it is only polylog(n).

  2. The slicing conjecture via small ball estimates

    math.FA 2025-01 conditional novelty 5.0 of 10

    An alternative proof of the slicing conjecture is given through optimal small-ball estimates for isotropic log-concave vectors, using stochastic localization and Guan's bound.

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