Existence of mean curvature flow singularities with bounded mean curvature

In “Curvature blow-up in perturbations of minimal cones evolving by mean curvature flow,” Velázquez constructed a countable collection flow solutions RN every dimension N?8. Each these becomes singular finite time at which the second fundamental form blows up. contrast, we confirm here that, N?8, infinitely many have uniformly bounded curvature.