Generalized Lagrangian mean curvature flows in almost Calabi-Yau manifolds

Abstract: In this paper, we study the generalized Lagrangian mean curvature flow in almost Einstein manifold proposed by T. Behrndt. We show that the singularity of this flow is characterized by the second fundamental form. We also show that the rescaled flow at a singularity converges to a finite union of Special Lagrangian cones for generalized Lagrangian mean curvature flow with zero-Maslov class in almost Calabi-Yau manifold. As a corollary, there is no finite time Type-I singularity for such a flow.