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 (Smoczyk et al. J für die reine und angewandte Mathematik 750: 97–121, 2019). By new estimates of derivatives along the flow, we weaken the initial condition and remove the positive curvature condition in Smoczyk et al. (J für die reine und angewandte Mathematik 750: 97–121, 2019). 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.