Logarithmic bounds for isoperimetry and slices of convex sets

By Bo'az Klartag. 2023

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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.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/18ce9f02a61f43d9233ab9a7c2d7fb04495a4d1f