  Let $n$ be an integer with $3 \leq n \leq 7$, and let $g$ be a Riemannian
metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$. We
establish an inequality relating the systole of the boundary to the infimum of
the mean curvature on the boundary. As a consequence, we obtain a new positive
energy theorem where equality holds for the Horowitz-Myers metrics.
