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MiS Preprint

Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials

Knut Smoczyk and Mu-Tao Wang


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.

MSC Codes:
lagrangian, mean curvature flow

Related publications

2003 Repository Open Access
Knut Smoczyk and Mu-Tao Wang

Mean curvature flows of Lagrangians submanifolds with convex potentials

In: Journal of differential geometry, 62 (2003) 2, pp. 243-257