Pith. sign in

REVIEW 8 cited by

A note on Bourgain's slicing problem

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2412.09075 v1 pith:JA4AIACD submitted 2024-12-12 math.MG

A note on Bourgain's slicing problem

Qingyang Guan This is my paper
classification math.MG
keywords slicingbourgainconstantnoteproblemboundeddecadefollowing
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

This note is to study Bourgain's slicing problem following the routes investigated in the last decade. We show that the slicing constant $L_n$ is bounded by $C\log(\log n) $, $n\geq 3$, for some universal constant $C$.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 8 Pith papers

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

  1. High-dimensional limits and extremizers for maximal functions associated with log-concave densities

    math.CA 2026-07 accept novelty 8.0

    All radial log-concave maximal function L^p norms converge to a universal limit λ(p) as dimension→∞, with the Euclidean ball asymptotically extremal.

  2. Nearly-Tight Bounds for Zonotope Containment and Beyond

    cs.DS 2026-05 unverdicted novelty 8.0

    Nearly-tight O(sqrt(d)) approximation for zonotope containment in the oracle model, with a proof of Talagrand's conjecture for constant Delta-modular zonotopes and a tight Theta(d/log d) bound for general convex bodies.

  3. Digesting the proof of the sharp thin-shell inequality

    math.MG 2026-07 accept novelty 7.0

    The optimal constant in the log-concave variance conjecture is E[(|X|²−n)²] ≤ 8n, attained by iid standard centered exponentials; a companion sharp bound holds for third moments and for the simplex among convex bodies.

  4. Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures

    math.MG 2026-05 unverdicted novelty 7.0

    Even log-concave measures satisfy μ(λK + (1-λ)L)^{c_n} ≥ λ μ(K)^{c_n} + (1-λ) μ(L)^{c_n} with c_n ≥ c/(n^3 ln n).

  5. Banach-Mazur distances and basis constants of isotropic log-concave random spaces

    math.FA 2026-04 unverdicted novelty 7.0

    Random normed spaces from isotropic log-concave measures satisfy d_BM >= cn / ln(1+m/n) with high probability, sharp in both parameters and recovering the order-n extremal when m is linear in n.

  6. Minimum Norm Interpolation via The Local Theory of Banach Spaces: The Role of Gaussianity

    math.ST 2026-07 conditional novelty 6.0

    The sharp MSE bound for the ℓ1-minimum-norm interpolator under isotropic Gaussian covariates is recovered via the geometry of symmetric Gaussian polytopes, without the convex Gaussian min-max theorem.

  7. Wasserstein bounds for denoising diffusion probabilistic models via the F\"ollmer process

    stat.ML 2026-05 unverdicted novelty 6.0

    Establishes dimension- and step-optimal Wasserstein bounds for DDPMs under Lipschitz score conditions and broad variance schedules via Föllmer process analysis, recovering prior results and extending to log-concave targets.

  8. Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures

    math.MG 2026-05 unverdicted novelty 6.0

    Proves dimensional Brunn-Minkowski inequality for even log-concave measures with c_n ≥ c/(n^3 ln n) and shows Γ_n ≈ n for maximal functional perimeter of isotropic log-concave measures.