  We prove that the Robin ground state and the Robin torsion function are
respectively log-concave and $\frac{1}{2}$-concave on an uniformly convex
domain $\Omega\subset \mathbb{R}^N$ of class $\mathcal{C}^m$, with $[m -\frac{
N}{2}]\geq 4$, provided the Robin parameter exceeds a critical threshold. Such
threshold depends on $N$, $m$, and on the geometry of $\Omega$, precisely on
the diameter and on the boundary curvatures up to order $m$.
