Convergence of Lagrangian mean curvature flow in K\"ahler-Einstein manifolds

TL;DR

This paper proves that Lagrangian mean curvature flow in K"ahler-Einstein manifolds converges under certain stability conditions, especially when starting from small perturbations of stable minimal Lagrangian submanifolds.

Contribution

It establishes convergence results for Lagrangian mean curvature flow in K"ahler-Einstein manifolds under specific stability assumptions, extending previous understanding.

Findings

Flow converges from small perturbations of stable minimal Lagrangian submanifolds.

Convergence holds under certain stability conditions in K"ahler-Einstein manifolds.

Provides new insights into the stability and long-term behavior of Lagrangian mean curvature flow.

Abstract

In this paper, we give some convergence results of Lagrangian mean curvature flow under some stability conditions in a general K\"ahler-Einstein manifold. In particular, we prove that the flow will converge if the initial data is some small perturbation of stable minimal Lagrangian submanifold in a K\"ahler-Einstein manifold.