Simplified Thomas–Yau conjecture for zero-Maslov-class Lagrangians

Let $M$ be a Calabi–Yau manifold and let $\Sigma$ be a compact embedded Lagrangian submanifold with zero Maslov class. Simplified Thomas–Yau conjecture. The mean curvature flow of $\Sigma$ exists for all time and converges smoothly to a special Lagrangian submanifold in the Hamiltonian isotopy class of $\Sigma$. This is presented as a simplified version of the Thomas–Yau conjecture because the original flow-stability condition is difficult to check and is not evidently preserved by Hamiltonian isotopies; the source describes it as a subject of considerable interest, with the general conjecture remaining open.