2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61337Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of a Calabi-Yau manifold. It involves a stability condition for graded Lagrangians, and can be proved for the simple case of $T^2$.31 pages, 3 figures; refereed and accepted for publication in "Symplectic Geometry and mirror symmetry: proceedings of a conference at KIAS, 2000."Differential GeometryHigh Energy Physics - TheoryAlgebraic GeometrySymplectic Geometry14J32text