WEIGHTED HAMILTONIAN STATIONARY LAGRANGIAN SUBMANIFOLDS AND GENERALIZED LAGRANGIAN MEAN CURVATURE FLOWS IN TORIC ALMOST CALABI-YAU MANIFOLDS

In this paper, we generalize examples of Lagrangian mean curvature flows constructed by Lee and Wang in C-m to toric almost Calabi-Yau manifolds. To be more precise, we construct examples of weighted Hamiltonian stationary Lagrangian submanifolds in toric almost Calabi-Yau manifolds and solutions of generalized Lagrangian mean curvature flows starting from these examples. We allow these flows to have some singularities and topological changes.