Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials

Knut Smoczyk, Mu-Tao Wang
2002 Journal of differential geometry  
This article studies the mean curvature flow of Lagrangian submanifolds. In particular, we prove the following global existence and convergence theorem: if the potential function of a Lagrangian graph in T 2n is convex, then the flow exists for all time and converges smoothly to a flat Lagrangian submanifold. We also discuss various conditions on the potential function that guarantee global existence and convergence.
doi:10.4310/jdg/1090950193 fatcat:pvqfhqrfxfhrfozimsnqbzyt7i