  In this paper we use structure preserving torus actions on Kahler-Einstein
manifolds to construct minimal Lagrangian submanifolds. Our main result is: Let
N^2n be a Kahler-Einstein manifold with positive scalar curvature with an
effective T^n-action. Then precisely one regular orbit L of the T-action is a
minimal Lagrangian submanifold of N. Moreover there is an (n-1)-torus T^n-1 in
T^n and a sequence of non-flat immersed minimal Lagrangian tori L_k in N,
invariant under T^n-1 s.t. L_k locally converge to L (in particular the
supremum of the sectional curvatures of L_k and the distance between L_k and L
go to 0 as k goes to infinity.
