Stability of the generalized Lagrangian mean curvature flow in cotangent bundle

Abstract: In this paper, we consider the stability of the generalized Lagrangian mean curvature flow of graph case in the cotangent bundle, which is first defined by Smoczyk-Tsui-Wang. By new estimates of derivatives along the flow, we weaken the initial condition and remove the positive curvature condition in Smoczyk-Tsui-Wang's work. More precisely, we prove that if the graph induced by a closed $1$-form is a special Lagrangian submanifold in the cotangent bundle of a Riemannian manifold, then the generalized Lagrangian mean curvature flow is stable near it.