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math.MG2026
Digesting the proof of the sharp thin-shell inequality
Yuansi Chen, Boaz Klartag
We present a proof that determines the optimal value of the universal constant in the thin-shell theorem for log-concave distributions in high dimensions. We prove that for any log…
math.MG2025
Distances between non-symmetric convex bodies: optimal bounds up to polylog
Pierre Bizeul, Boaz Klartag
In this paper we determine, up to polylogarithmic factors, the diameter of the Banach--Mazur compactum of -dimensional convex bodies without symmetry assumptions. We prove that…
math.MG2024★ 1 cited
Affirmative Resolution of Bourgain's Slicing Problem using Guan's Bound
Boaz Klartag, Joseph Lehec
We provide the final step in the resolution of Bourgain's slicing problem in the affirmative. Thus we establish the following theorem: for any convex body $K \subseteq \mathbb{R}^n…