Author

Kai-Wen Yang

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Preprint Aug 2026

The Brunn--Minkowski inequality for the Gaussian measure

Let $\gamma_n$ be the standard Gaussian measure on $\mathbb{R}^n$, $n\ge2$, and let $\alpha_\gamma(n)$ be the largest number for which \[ \gamma_n(\lambda K+(1-\lambda)L)^{\alpha_\gamma(n)} \ge \lambda\gamma_n(K)^{\alpha_\gamma(n)} +(1-\lambda)\gamma_n(L)^{\alpha_\gamma(n)} \] holds for all convex bodies $K,L\subset\ma...

Kai-Wen Yang · 0 citations

Preprint Jul 2026

A uniform bound in the dimensional Brunn--Minkowski inequality for even log-concave measures

For every $n\ge 2$, we prove that there exists an exponent $p_n$ such that, for every even log-concave probability measure $\mu$ on $\mathbb R^n$, all nonempty symmetric convex sets $K,L\subseteq\mathbb R^n$, and all $\lambda\in[0,1]$, $$ \mu(\lambda K+(1-\lambda)L)^{p_n} \ge \lambda\mu(K)^{p_n}+(1-\lambda)\mu(L)^{p_n}...

Kai-Wen Yang · 0 citations