A Dimension-Free Hermite-Hadamard Inequality via Gradient Estimates for the Torsion Function

Jianfeng Lu, Stefan Steinerberger

Let $\Omega \subset {\mathbb{R}}^n$ be a convex domain and let $f:\Omega \to \mathbb{R}$ be a subharmonic function, $\Delta f\ge 0$, which satisfies $f\ge 0$ on the boundary $\partial \Omega$.…