A. Stancu

Failure of a Brunn-Minkowski-type inequality for the Gaussian torsional rigidity

Let $u$ be the torsion function for the Ornstein-Uhlenbeck operator on a bounded domain $\Omega \subset \mathbb{R}^n$, i.e., the solution of $\Delta u - x \cdot \nabla u = -1$ in $\Omega$ with $u = 0$ on $\partial\Omega$. Let $T_\gamma(\Omega) = \int_\Omega u \, d\gamma$ be the Gaussian torsional rigidity. We prove tha...