Longtime existence of the Lagrangian mean curvature flow

  • Knut SmoczykEmail author


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-Ampére 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.


Curvature Flow Lagrangian Submanifold Natural Assumption Flat Space Independent Proof 
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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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