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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
71/2002

Longtime existence of the Lagrangian mean curvature flow

Knut Smoczyk

Abstract

Given a compact Lagrangian submanifold in flat space evolving by its mean curvature, we prove uniform $C^{2,\alpha}$-bounds in space and $C^2$-estimates in time for the underlying Monge-Ampère equation under weak and natural assumptions on the initial Lagrangian submanifold. This implies longtime existence and convergence of the Lagrangian mean curvature flow. In the $2$-dimensional case we can relax our assumptions and obtain two independent proofs for the same result.

Received:
Aug 20, 2002
Published:
Aug 20, 2002
MSC Codes:
53C44
Keywords:
lagrangian, mean curvature flow

Related publications

inJournal
2004 Repository Open Access
Knut Smoczyk

Longtime existence of the Lagrangian mean curvature flow

In: Calculus of variations and partial differential equations, 20 (2004) 1, pp. 25-46