The positive energy conjecture for a class of AHM metrics on $mathbb{R}^{2}timesmathbb{T}^{n-2}$

We prove the positive energy conjecture for a class of asymptotically Horowitz-Myers metrics on $mathbb{R}^{2}timesmathbb{T}^{n-2}$. This generalizes the previous results of Barzegar-Chru{s}ciel-H{o}rzinger-Maliborski-Nguyen as well as the authors.