Convergence of cohomogeneity-one Lagrangian mean curvature flow in positive Kähler-Einstein manifolds

We prove that Lagrangian mean curvature flow starting from a closed, embedded, cohomogeneity-one Lagrangian in a closed, positive Kähler--Einstein manifold exists for all time, remains embedded, and converges smoothly and graphically to a minimal Lagrangian, under natural exactness and regularity as