Systolic inequalities and the Horowitz-Myers conjecture

Let 3 ≤ n ≤ 7, and let g be a Riemannian metric on B² × Tⁿ⁻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 confirm a conjecture of Horowitz and Myers.