Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials

Knut Smoczyk, and Mu-Tao Wang
(Please use for correspondence this email).

Submission date: 11. Oct. 2002
Pages: 18
published in: Journal of differential geometry, 62 (2003) 2, p. 243-257 
MSC-Numbers: 53C44
Keywords and phrases: lagrangian, mean curvature flow
Download preprint: PDF (174 kB), PS ziped (171 kB)

Abstract:
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.