Author

Zhao-Kai Song

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Preprint Oct 2026

An $O(1)$ Bound for the KLS Constant

The Kannan--Lov\'asz--Simonovits (KLS) conjecture asks whether every isotropic log-concave probability measure on $\mathbb R^n$ has a Cheeger constant bounded below by a universal positive constant. We prove that $\psi_n\le C$ for a universal constant $C>0$, resolving the KLS conjecture. We also prove that $C_P(\mu)\le...

Zhao-Kai Song, Xin-Zhi Zhang · 0 citations