2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61338We make a conjecture about mean curvature flow of Lagrangian submanifolds of Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the stability condition, and propose a Jordan-Hölder-type decomposition of (special) Lagrangians. The main results are the uniqueness of special Lagrangians in hamiltonian deformation classes of Lagrangians, under mild conditions, and a proof of the conjecture in some cases with symmetry: mean curvature flow converging to Shapere-Vafa's examples of SLags.36 pages, 4 figures. Minor referee's correctionsDifferential GeometryHigh Energy Physics - TheoryAlgebraic GeometrySymplectic Geometry14J32; 53C44text