  We prove regularity, global existence, and convergence of Lagrangian mean
curvature flows in the two-convex case. Such results were previously only known
in the convex case, of which the current work represents a significant
improvement. The proof relies on a newly discovered monotone quantity that
controls two-convexity. Through a unitary transformation, same result for the
mean curvature flow of area-decreasing Lagrangian submanifolds were
established.
