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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
92/2002

Mean Curvature Flows of Lagrangian Submanifolds with Convex Potentials

Knut Smoczyk and Mu-Tao Wang

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 $T^{2n}$ 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.

Received:
Oct 11, 2002
Published:
Oct 11, 2002
MSC Codes:
53C44
Keywords:
lagrangian, mean curvature flow

Related publications

inJournal
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