Publications
2002
Issue 71

MiS Preprint Repository

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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 $C^{2, α}$ -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.

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Received:: 20.08.02

Published:: 20.08.02

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

BibTex DOI: 10.1007/s00526-003-0226-9