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arXiv · 2303.14938

Logarithmic bounds for isoperimetry and slices of convex sets

Bo'az Klartag
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Abstract

We prove that the Bourgain slicing conjecture and the Kannan-Lov\'asz-Simonovits (KLS) isoperimetric conjecture in $\mathbb{R}^n$ hold true up to a factor of $\sqrt{\log n}$. A new ingredient used in the proof is an improved log-concave Lichnerowicz inequality.

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Bo'az Klartag. 2023-03-27. Logarithmic bounds for isoperimetry and slices of convex sets. https://arxiv.org/abs/2303.14938

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