Journal of Differential Geometry

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 T2n 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.

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J. Differential Geom., Volume 62, Number 2 (2002), 243-257.

First available in Project Euclid: 27 July 2004

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Smoczyk, Knut; Wang, Mu-Tao. Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials. J. Differential Geom. 62 (2002), no. 2, 243--257. doi:10.4310/jdg/1090950193.

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