Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials
Knut Smoczyk and Mu-Tao Wang
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Submission date: 11. Oct. 2002
published in: Journal of differential geometry, 62 (2003) 2, p. 243-257
Keywords and phrases: lagrangian, mean curvature flow
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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 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.