Conformal tori with almost non-negative scalar curvature

In this work, we consider sequence of metrics with almost non-negative scalar curvature on torus. We show that if the is uniformly conformal to another bounded Ricci geometry, then it converges a flat metric in volume preserving intrinsic sense, measured Gromov–Hausdorff sense and $$L^p$$ sense. Moreover, similar stability also holds manifolds non-positive Yamabe invariant.